二階拋物微分方程

內(nèi)容概要

二階拋物微分方程，ISBN：9787506259606，作者：G.M.Lieberman

書籍目錄

PrefaceChapter Ⅰ. Introduction  1 Outline of this book  2 Further Remarks  3 NotationChapterⅡ. Maximum Principles  1 The Weak maximum Principles  2 The strong maximum principle  3 A priori estimates  Notes  ExercisesChapter Ⅲ. Introduction to the Theory of weak Solutions  1 The theory of weak derivatives  2 The method of continuity  3 Problems in small balls  4 Global existence and the Peron process  Notes  ExercisesChapter Ⅳ. Holder Estimates  1 Holder conbtinuity  2 Campanato spaces  3 Interior estimates  4 Estimates near a flat boumdary  5 Regularized distance  6 Intermediate Schauder Estimates  7 Curved boundaries and nonzero boundary data  8 A special mixed problem  Notes  ExercisesChapter Ⅴ. Existence, Uniqueness, and Regularity of Solutions  1 Uniqueness of Solutions  2 The Cauchy-Dirichlet problem with bounded coefficients  3 The Cquchy-Dirichlet problem with unbounded coefficients  4 The obliquederivative problem  Notes  ExercisesChapter Ⅵ. Further Theory of Weak Solutions……Chapter Ⅶ. Strong SolutionsChapter Ⅷ. Fixed Point Theorems and TheirChapter Ⅸ. Comparison and Maximum PrinciplesChapter Ⅹ Boundary Gradient ExtimatesChapter Ⅺ. Global and Local Gradient BoundsChapter XII. Holder Gradient Extimates and Existence TheoremsChapter XIII. The Oblique Derivative Problem for Quasilinear Parabolic EquationsChapter XIV. Fully Nonlinear EquationsⅠ.Chapter XV Fully Nonlinear Equations Ⅱ.References Index

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