Geodesic
Nonhomogeneous boundary conditions for the spectral fractional Laplacian
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 439-467 Cet article a éte moissonné depuis la source Numdam

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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 the boundary. This is used to establish and solve boundary value problems associated with nonhomogeneous boundary conditions. We provide a weak-L1 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.

DOI : 10.1016/j.anihpc.2016.02.001
Classification : 35B40, 35B30, 45P05, 35C15
Keywords: Spectral fractional Laplacian, Dirichlet problem, Boundary blow-up solutions, Large solutions 
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     author = {Abatangelo, Nicola and Dupaigne, Louis},
     title = {Nonhomogeneous boundary conditions for the spectral fractional {Laplacian}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {439--467},
     year = {2017},
     publisher = {Elsevier},
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     number = {2},
     doi = {10.1016/j.anihpc.2016.02.001},
     mrnumber = {3610940},
     zbl = {1372.35327},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2016.02.001/}
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Abatangelo, Nicola; Dupaigne, Louis. Nonhomogeneous boundary conditions for the spectral fractional Laplacian. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 439-467. doi: 10.1016/j.anihpc.2016.02.001

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