In this paper we study a linear elliptic equation having mixed boundary conditions, defined in a connected open set Ω of R n. We prove a comparison result with a suitable symmetrized'' Dirichlet problem which cannot be uniformly elliptic depending on the regularity of ∂ Ω. Regularity results for non-uniformly elliptic equations are also given.
Brandolini B., Posteraro M R, Volpicelli R (2003). Comparison results for a linear elliptic equation with mixed boundary conditions. DIFFERENTIAL AND INTEGRAL EQUATIONS, 16(5), 625-639.
Comparison results for a linear elliptic equation with mixed boundary conditions
Brandolini B.;
2003-01-01
Abstract
In this paper we study a linear elliptic equation having mixed boundary conditions, defined in a connected open set Ω of R n. We prove a comparison result with a suitable symmetrized'' Dirichlet problem which cannot be uniformly elliptic depending on the regularity of ∂ Ω. Regularity results for non-uniformly elliptic equations are also given.
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