SMOOTHNESS OF SOLUTIONS OF DEGENERATING ELLIPTIC EQUATIONS

Abstract

It is proven that the generalized solution of boundary-value problems for degenerating second-order equations satisfies Holder's boundary condition under broad assumptions. An example is given, showing that a greater smoothness of the solutions cannot be achieved only by increasing the smoothness of the data given in the problem. Conditions for the existence of derivatives of the generalized solution are clarified. The investigation is carried out by means of probability methods.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 22, 1969
Accession Number
AD0700353

Entities

People

  • M. F. Freidlin

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Brownian Motion
  • Cauchy Problem
  • Coefficients
  • Coordinate Systems
  • Diameters
  • Differential Equations
  • Diffusion
  • Equations
  • Inequalities
  • Integrals
  • Markov Processes
  • Probability
  • Random Variables
  • Trajectories

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Systems Analysis and Design