On the Analyticity of the Solutions of Linear Elliptic Systems of Partial Differential Equations

摘要

The property of analyticity of solutions of elliptic partial differential equations with analytic coefficients is well known. An elegant proof, and also references to earlier proofs, may be found in the book by P. John [6]. In this paper we consider (strongly) elliptic equations in a domain with analytic boundary and prove analyticity at the boundary of solutions with analytic Dirichlet data. In the last section we also indicate how our method of proof yields a new derivation of analyticity of solutions of general analytic elliptic systems at interior points of a domain.