Solution of a degenerated elliptic equation of second order in an unbounded domain

  • Werner Berndt

    Universität Leipzig, Germany

Abstract

The paper deals with the equation div in , where and are given smooth functions. The equation degenerates on the smooth surface where behaves like a power of dist . The following results are proved: 1. Existence and uniqueness (up to additive constants) of a solution with ; the proof uses a variational method in a weighted Sobolev space; 2. Regularity of the solution near ; 3. Convergence and correctness of a numerical (difference) method; 4. Convergence of an iteration method to solve the discrete problem.

Cite this article

Werner Berndt, Solution of a degenerated elliptic equation of second order in an unbounded domain. Z. Anal. Anwend. 1 (1982), no. 3, pp. 53–68

DOI 10.4171/ZAA/19