The dirichlet problem in a domain whose boundary is partly degenerated

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In this paper we bring a formulation of the Dirichlet problem for strongly elliptic equations in domains vhose boundaries may include manifolds of different dimensions. It is shown that, under certain regularity conditions, this problem is equivalent to the generalized Dirichlèt problem, with respect to existence and uniquennes of solutions.


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Additional information

This paper represents part of a thesis submitted to the Senate of the Technion, Israel Institute of Technology, in partial fulfillment of the requirements for the degree of Doctor of Science. The author wishes to tank ProfessorS. Agmon for his gudance and help in the preparation of this work.

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Marcus, M. The dirichlet problem in a domain whose boundary is partly degenerated. Annali di Matematica 73, 159–194 (1966).

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  • Elliptic Equation
  • Dirichlet Problem
  • Regularity Condition