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Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

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Abstract

Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

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Authors and Affiliations

  1. Department of Applied Analysis and Computational Mathematics & MTA ELTE NumNet Research Group, Eötvös Loránd University, Pázmány P. stny. 1C–1117, Budapest, Hungary

    Ferenc Izsák

  2. Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Pázmány P. stny. 1C–1117, Budapest, Hungary

    Gábor Maros

Authors
  1. Ferenc Izsák
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  2. Gábor Maros
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Correspondence to Ferenc Izsák.

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Izsák, F., Maros, G. Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions. Fract Calc Appl Anal 23, 378–389 (2020). https://doi.org/10.1515/fca-2020-0018

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  • DOI: https://doi.org/10.1515/fca-2020-0018

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