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The Third Problem for the Laplace Equation with a Boundary Condition from L p

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Abstract.

The third problem for the Laplace equation is studied on an open set with Lipschitz boundary. The boundary condition is in L p and it is fulfilled in the sense of the nontangential limit. The existence and the uniqueness of a solution is proved and the solution is expressed in the form of a single layer potential. For domains with C 1 boundary the explicit solution of the problem is calculated.

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Authors and Affiliations

  1. Academy of Sciences of the Czech Republic, Mathematical Institute, Žitná 25, 115 67, Praha 1, Czech Republic

    Dagmar Medková

  2. Faculty of Mechanical Engineering, Department of Technical Mathematics, Czech Technical University, Karlovo nám. 13, 121 35, Praha 2, Czech Republic

    Dagmar Medková

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  1. Dagmar Medková
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Correspondence to Dagmar Medková.

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Medková, D. The Third Problem for the Laplace Equation with a Boundary Condition from L p . Integr. equ. oper. theory 54, 235–258 (2006). https://doi.org/10.1007/s00020-003-1354-5

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  • DOI: https://doi.org/10.1007/s00020-003-1354-5

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