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Asymptotic Analysis of Periodic Structures

Preface.- 1. The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions.- 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators.- 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity.- 4. L^p Spaces.- 5. Hilbert Spaces.- 6. Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators.- 7. The Hille-Yosida Theorem.- 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension.- 9. Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions.- 10. Evolution Problems: The Heat Equation and the Wave Equation.- 11. Some Complements.- Problems.- Solutions of Some Exercises and Problems.- Bibliography.- Index.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II

Publisher Summary This chapter examines viscosity solutions of Hamilton–Jacobi equations. The ability to formulate an existence and uniqueness result for generality requires the ability to discuss non differential solutions of the equation, and this has not been possible before. However, the existence assertions can be proved by expanding on the arguments in the introduction concerning the relationship of the vanishing viscosity method and the notion of viscosity solutions, so users can adapt known methods here. The uniqueness is then the main new point.

https://www.ams.org/tran/1983-277-01/S0002-9947-1983-0690039-8/S0002-9947-1983-0690039-8.pdf

Avron Douglis

Papers

Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II

Interior estimates for elliptic systems of partial differential equations

A function-theoretic approach to elliptic systems of equations in two variables†

Some existence theorems for hyperbolic systems of partial differential equations in two independent variables

The continuous dependence of generalized solutions of non‐linear partial differential equations upon initial data