Techniques in Linear and Nonlinear PDE's

Abstract

Problems studied included existence and properties of solutions of nonlinear partial differential equations, including applications to shock waves and to differential geometry covering a very wide range of subjects. Variational approaches for an elliptic boundary value problem with nonlinear forcing term a(x)g(u) were developed. The function a is allowed to change sign. New variational arguments to obtain positive solutions were introduced. Ref. 6 treats related problems using degree theory. In 5 and extended in 9 it was shown that for a constrained variational problem local C1 minima are also H1 local minima. This is used to obtain multiple solutions for a class of problems. In 3 new results on existence and properties of principal eigenvalue for a general second order elliptic operator under Dirichlet conditions are obtained for arbitrary domains.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1995
Accession Number
ADA389475

Entities

People

  • Louis Nirenberg

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Differential Geometry
  • Eigenvalues
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Geometry
  • New York
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Shock Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Structural Dynamics.