Positive Solutions of Nonlinear Elliptic Equations in the Euclidean Plane

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ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (393 download)

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Book Synopsis Positive Solutions of Nonlinear Elliptic Equations in the Euclidean Plane by : Ünal Ufuktepe

Download or read book Positive Solutions of Nonlinear Elliptic Equations in the Euclidean Plane written by Ünal Ufuktepe and published by . This book was released on 1996 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present thesis, we study the existence of solutions to the problem $\Delta u+f(x, u)=0$ in D $u>0$ in D $u=0$ on $\partial D$ (0.1) where D is an unbounded domain in $\IR\sp2$ with a compact non-empty boundary $\partial D$ consisting of finitely many Jordan curves. The goal is to prove an existence theorem for problem (0.1) in a general setting by using Brownian path integration and potential theory. In the first chapter, we provide the necessary background for the following chapters. The second chapter is devoted to the Feynman-Kac functional, Schrodinger equations, and the conditional Brownian motion. In the third chapter, we first introduce the positive harmonic function in D with the specified behavior around $\partial D$ and $\{\infty\}.$ We prove the uniform integrability of the family of functions $\{G\sb{D}(x, .)\vert q(.):x\in D\}$ for a function q belonging to a general class $K\sbsp{2}{\infty}, $ where $G\sb{D}(., .)$ is the Green function in D. Finally we prove the main theorem which solves problem (0.1) under certain conditions on f.

Positive Solutions to Nonlinear Elliptic Equations with Prescribed Singularities

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ISBN 13 :
Total Pages : 394 pages
Book Rating : 4.:/5 (33 download)

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Book Synopsis Positive Solutions to Nonlinear Elliptic Equations with Prescribed Singularities by : David Lloyd Finn

Download or read book Positive Solutions to Nonlinear Elliptic Equations with Prescribed Singularities written by David Lloyd Finn and published by . This book was released on 1995 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fully Nonlinear Elliptic Equations

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Publisher : American Mathematical Soc.
ISBN 13 : 0821804375
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fully Nonlinear Elliptic Equations by : Luis A. Caffarelli

Download or read book Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

Singular Solutions of Nonlinear Elliptic and Parabolic Equations

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110390086
Total Pages : 531 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Singular Solutions of Nonlinear Elliptic and Parabolic Equations by : Alexander A. Kovalevsky

Download or read book Singular Solutions of Nonlinear Elliptic and Parabolic Equations written by Alexander A. Kovalevsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-03-21 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography

Positive Solutions to Nonlinear Elliptic Equations with Critical Potential

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ISBN 13 :
Total Pages : 143 pages
Book Rating : 4.:/5 (931 download)

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Book Synopsis Positive Solutions to Nonlinear Elliptic Equations with Critical Potential by :

Download or read book Positive Solutions to Nonlinear Elliptic Equations with Critical Potential written by and published by . This book was released on 2006 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Existence of Positive Solutions for Nonlinear Elliptic Equations with Convection Terms

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (15 download)

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Book Synopsis Existence of Positive Solutions for Nonlinear Elliptic Equations with Convection Terms by :

Download or read book Existence of Positive Solutions for Nonlinear Elliptic Equations with Convection Terms written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents

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ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents by : Haim Brezis

Download or read book Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents written by Haim Brezis and published by . This book was released on 1983 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multiple Positive Solutions on Nonlinear Elliptic Equations Involving Critical Sobolev Exponents

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ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (246 download)

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Book Synopsis Multiple Positive Solutions on Nonlinear Elliptic Equations Involving Critical Sobolev Exponents by : Monica Lazzo

Download or read book Multiple Positive Solutions on Nonlinear Elliptic Equations Involving Critical Sobolev Exponents written by Monica Lazzo and published by . This book was released on 1991 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Number of Positive Solutions of Weakly Nonlinear Elliptic Equations when a Parameter is Large

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ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (216 download)

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Book Synopsis On the Number of Positive Solutions of Weakly Nonlinear Elliptic Equations when a Parameter is Large by : E. N. Dancer

Download or read book On the Number of Positive Solutions of Weakly Nonlinear Elliptic Equations when a Parameter is Large written by E. N. Dancer and published by . This book was released on 1984 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Elliptic Equations and Nonassociative Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 1470417103
Total Pages : 250 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonlinear Elliptic Equations and Nonassociative Algebras by : Nikolai Nadirashvili

Download or read book Nonlinear Elliptic Equations and Nonassociative Algebras written by Nikolai Nadirashvili and published by American Mathematical Soc.. This book was released on 2014-12-03 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions where nonclassical homogeneous solutions to fully nonlinear uniformly elliptic equations do exist; this should be compared with the situation of, say, ten years ago when the very existence of nonclassical viscosity solutions was not known.

Positive Global Solutions of Nonlinear Elliptic Equations

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ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (657 download)

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Book Synopsis Positive Global Solutions of Nonlinear Elliptic Equations by : Yin Xi Huang

Download or read book Positive Global Solutions of Nonlinear Elliptic Equations written by Yin Xi Huang and published by . This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators

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Publisher : Nova Publishers
ISBN 13 : 9781590333761
Total Pages : 424 pages
Book Rating : 4.3/5 (337 download)

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Book Synopsis Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators by : István Faragó

Download or read book Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators written by István Faragó and published by Nova Publishers. This book was released on 2002 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators - Theory & Applications

Pairs of Positive Solutions on Nonlinear Elliptic Partial Differential Equations

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ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis Pairs of Positive Solutions on Nonlinear Elliptic Partial Differential Equations by : P. H. Rabinowitz

Download or read book Pairs of Positive Solutions on Nonlinear Elliptic Partial Differential Equations written by P. H. Rabinowitz and published by . This book was released on 1972 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Existence of Positive Entire Solutions of Nonlinear Elliptic Equations

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ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (59 download)

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Book Synopsis On the Existence of Positive Entire Solutions of Nonlinear Elliptic Equations by : Marco Squassina

Download or read book On the Existence of Positive Entire Solutions of Nonlinear Elliptic Equations written by Marco Squassina and published by . This book was released on 2000 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Boundary Growth of Superharmonic Functions and Positive Solutions of Nonlinear Elliptic Equations

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ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (675 download)

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Book Synopsis The Boundary Growth of Superharmonic Functions and Positive Solutions of Nonlinear Elliptic Equations by :

Download or read book The Boundary Growth of Superharmonic Functions and Positive Solutions of Nonlinear Elliptic Equations written by and published by . This book was released on 2006 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Second Order Elliptic Equations

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Publisher : Springer Nature
ISBN 13 : 9819986923
Total Pages : 319 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Nonlinear Second Order Elliptic Equations by : Mingxin Wang

Download or read book Nonlinear Second Order Elliptic Equations written by Mingxin Wang and published by Springer Nature. This book was released on with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Positive Solutions Obtained as Local Minima Via Symmetries, for Nonlinear Elliptic Equations

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ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (483 download)

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Book Synopsis Positive Solutions Obtained as Local Minima Via Symmetries, for Nonlinear Elliptic Equations by : Florin Catrina

Download or read book Positive Solutions Obtained as Local Minima Via Symmetries, for Nonlinear Elliptic Equations written by Florin Catrina and published by . This book was released on 2000 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: