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- catalog abstract ""This is the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric."--Jacket.".
- catalog contributor b11650734.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description ""This is the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric."--Jacket.".
- catalog description "Includes bibliographical references (p. 332-336) and index.".
- catalog description "Some Notation, Terminology and Basic Calculus -- 1. Introduction -- 2. Some Maximum Principles for Elliptic Equations -- 3. Symmetry for a Non-linear Poisson Equation in a Symmetric Set [Omega] -- 4. Symmetry for the Non-linear Poisson Equation in R[superscript N] -- 5. Monotonicity of Positive Solutions in a Bounded Set [Omega] -- App. A. On the Newtonian Potential -- App. B. Rudimentary Facts about Harmonic Functions and the Poisson Equation -- App. C. Construction of the Primary Function of Siegel Type -- App. D. On the Divergence Theorem and Related Matters -- App. E. The Edge-Point Lemma.".
- catalog extent "x, 340 p. ;".
- catalog identifier "0521461952".
- catalog isPartOf "Cambridge tracts in mathematics ; 128.".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "Cambridge : Cambridge University Press,".
- catalog subject "515.353 21".
- catalog subject "Differential equations, Elliptic Problems, exercises, etc.".
- catalog subject "Differential equations, Elliptic.".
- catalog subject "Maximum principles (Mathematics)".
- catalog subject "QA377 .F73 2000".
- catalog subject "Symmetry.".
- catalog tableOfContents "Some Notation, Terminology and Basic Calculus -- 1. Introduction -- 2. Some Maximum Principles for Elliptic Equations -- 3. Symmetry for a Non-linear Poisson Equation in a Symmetric Set [Omega] -- 4. Symmetry for the Non-linear Poisson Equation in R[superscript N] -- 5. Monotonicity of Positive Solutions in a Bounded Set [Omega] -- App. A. On the Newtonian Potential -- App. B. Rudimentary Facts about Harmonic Functions and the Poisson Equation -- App. C. Construction of the Primary Function of Siegel Type -- App. D. On the Divergence Theorem and Related Matters -- App. E. The Edge-Point Lemma.".
- catalog title "An introduction to maximum principles and symmetry in elliptic problems / L.E. Fraenkel.".
- catalog type "Problems, exercises, etc. fast".
- catalog type "text".