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A priori bounds in \(L^p\) for solutions of elliptic equations in divergence form. (English) Zbl 1286.35092
This paper proves an \(L^p\) (\(p>1\)) a priori bound for the solutions of the Dirichlet problem for second order linear PDEs in divergence form.The authors allow discontinuous coefficients as well as unbounded domains.
Their existence results use Morrey spaces (adapted to unbounded domains) and a generalisation of a lemma by Stampaccia on non-negative decreasing functions.

MSC:
35J25 Boundary value problems for second-order elliptic equations
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