Dirichlet problem for degenerate elliptic equations

Avner Friedman, Mark A. Pinsky

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let L0 be a degenerate second order elliptic operator with no zeroth order term in an m-dimensional domain G9 and let L = L0 + c. One divides the boundary of G into disjoint sets ∑1,∑2, ∑3,∑3the non characteristic part, and on ∑2 the "drift” is outward. When c is negative, the following Dirichlet problem has been considered in the literature: Lu =0 in G, u is prescribed on ∑2u ∑3. In the present work it is assume that c ≤ 0. Assuming additional boundary conditions on a certain finite number of points of ∑1, a unique solution of the Dirichlet problem is established.

Original languageEnglish (US)
Pages (from-to)359-383
Number of pages25
JournalTransactions of the American Mathematical Society
Volume186
DOIs
StatePublished - Dec 1973

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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