Elliptic Partial Differential Equa-tions of Second Order

  title={Elliptic Partial Differential Equa-tions of Second Order},
  author={D. Gilbarg and N. Trudinger},
Chapter 1. Introduction Part I: Linear Equations Chapter 2. Laplace's Equation 2.1 The Mean Value Inequalities 2.2 Maximum and Minimum Principle 2.3 The Harnack Inequality 2.4 Green's Representation 2.5 The Poisson Integral 2.6 Convergence Theorems 2.7 Interior Estimates of Derivatives 2.8 The Dirichlet Problem the Method of Subharmonic Functions 2.9 Capacity Problems Chapter 3. The Classical Maximum Principle 3.1 The Weak Maximum Principle 3.2 The Strong Maximum Principle 3.3 Apriori Bounds 3… Expand
Linear Elliptic Differential Equations
At first, we transform boundary value problems for elliptic differential equations with two independent variables into a Riemann-Hilbert boundary value problem in Section 1. The latter can be solvedExpand
Variational Methods for Nonlocal Fractional Problems
Foreword Jean Mawhin Preface Part I. Fractional Sobolev Spaces: 1. Fractional framework 2. A density result for fractional Sobolev spaces 3. An eigenvalue problem 4. Weak and viscosity solutions 5.Expand
Boundary Hölder regularity for elliptic equations
This paper investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. We prove by a new unified method the pointwiseExpand
Elliptic Boundary Value Problems
This chapter treats some basic results of classical theory of elliptic boundary value problems with main emphasis on the existence for the Dirichlet problem in the space C 2(Ω) ∩ C(Ω). The DirichletExpand
Boundary value problems for elliptic partial differential equations
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partialExpand
Interior Hölder Estimates for Second Derivatives
This chapter is concerned with interior Holder regularity of second derivatives of solutions to the Monge–Ampere equation where \(\Omega\) is a bounded convex domain in \(\mathbb{R}^{n}\). The mainExpand
A comparison principle for a class of fourth-order elliptic operators
There is a vast literature concerning comparison principles of various types for ordinary and partial differential equations and for systems of such equations. Many of these results are forExpand
CHAPTER 6 - Maximum Principles for Elliptic Partial Differential Equations
This chapter presents explanations of the various maximum principles available for elliptic second order equations, from their beginnings in linear theory to nonlinear equations, operators, andExpand
Chapter 5 Schauder-type estimates and applications
Publisher Summary The Schauder estimates are among the oldest and most useful tools in the modern theory of elliptic partial differential equations (PDEs). Their influence may be felt in practicallyExpand
Existence theorems for some nonlinear fourth order elliptic boundary value problems
The general outline of our method is to that of of the second author second order elliptic parabolic equations [S, 71. of our effort is in deriving estimates for linear equations which lead to forExpand