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AuthorGilbarg, David. author
TitleElliptic Partial Differential Equations of Second Order [electronic resource] / by David Gilbarg, Neil S. Trudinger
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2001
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Descript XIII, 518 p. online resource


From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathรฉmatiques Pures et Appliquรฉes,1985


1. Introduction -- I. Linear Equations -- 2. Laplaceโ{128}{153}s Equation -- 3. The Classical Maximum Principle -- 4. Poissonโ{128}{153}s Equation and the Newtonian Potential -- 5. Banach and Hubert Spaces -- 6. Classical Solutions; the Schauder Approach -- 7. Sobolev Spaces -- 8. Generalized Solutions and Regularity -- 9. Strong Solutions -- II. Quasilinear Equations -- 10. Maximum and Comparison Principles -- 11. Topological Fixed Point Theorems and Their Application -- 12. Equations in Two Variables -- 13. Hรถlder Estimates for the Gradient -- 14. Boundary Gradient Estimates -- 15. Global and Interior Gradient Bounds -- 16. Equations of Mean Curvature Type -- 17. Fully Nonlinear Equations -- Epilogue -- Notation Index

Mathematics Partial differential equations Mathematics Partial Differential Equations


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