Abstract
Building on the a priori estimates established in [ 3 ], we obtain a priori estimates for classical solutions to ellipticproblems with Dirichlet boundary conditions on regions with convex-starlike boundary. This includes ring-like regions. Arguments that go back to [ 4 ] are used to prove a priori bounds near the convex part of the boundary.Using that the boundary term in the Pohozaev identity on the boundary of a star-like region does not change sign, the proof isconcluded.
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