Nonhomogeneous boundary conditions for the spectral fractional Laplacian

Abstract : We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at boundary. This is used to establish and solve boundary value problems associated with nonhomogeneous boundary conditions. We provide a weak-L 1 theory to show how problems with measure data at the boundary and inside the domain are well-posed. We study linear and semilinear problems, performing a sub-and supersolution method. We finally show the existence of large solutions for some power-like nonlinearities.
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Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2016, 〈10.1016/j.anihpc.2016.02.001〉
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Nicola Abatangelo, Louis Dupaigne. Nonhomogeneous boundary conditions for the spectral fractional Laplacian. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2016, 〈10.1016/j.anihpc.2016.02.001〉. 〈hal-01283983〉

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