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arXiv · 1911.05194

Equivalence of the Dirichlet and Neumann problems for the Laplace operator in planar doubly-connected regions

Claudiu Dinicu
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Abstract

Motivated by recent results regarding the equivalence of the Dirichlet and Neumann problems for the Laplace operator in the case of simply connected regions, the present paper takes a step further and provides a similar equivalence between the above mentioned problems in the case of planar doubly-connected regions. The equivalence means that solving any of these problems leads by an explicit formula to a solution of the other problem. In addition, suffcient conditions guaranteeing the uniform Holder continuity of the higher order partial derivatives of the solutions to the Neumann problem are provided as a consequence of this equivalence.

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Claudiu Dinicu. 2020-05-11. Equivalence of the Dirichlet and Neumann problems for the Laplace operator in planar doubly-connected regions. https://arxiv.org/abs/1911.05194

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