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Note on a sign-dependent regularity for the polyharmonic Dirichlet problem

A priori estimates for semilinear higher order elliptic equations usually have to deal with the absence of a maximum principle. This note presents some regularity estimates for the polyharmonic Dirichlet problem that will make a distinction between the influence on the solution of the positive and the negative part of the right-hand side.

preprint2020arXivOpen access
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