Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

Izsák, Ferenc and Maros, Gábor (2020) Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 23 (2). pp. 378-389. ISSN 1314-2224

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Abstract

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

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