Nonlocal operatorExtension theoremHarmonic functionWe prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem. We give a Douglas-type formula for the quadratic ...
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Extension and trace for nonlocal operatorsArtur RutkowskiKatarzyna Pietruska-PaubaKrzysztof BogdanTomasz Grzywny
We study function spaces and extension results in relation with Dirichlet\nproblems involving integrodifferential operators. For such problems, data are\nprescribed on the complement of a given domain in the Euclidean space. We\nintroduce a function space that serves as a trace space for nonlocal...
We study function spaces and extension results in relation with Dirichlet problems involving integrodifferential operators. For such problems, data are prescribed on the complement of a given domain Omega subset of R-d. We introduce a function space that serves as a trace space for nonlocal ...
We study function spaces and extension results in relation with Dirichlet problems involving integrodifferential operators. For such problems, data are prescribed on the complement of a given domain 惟?Rd. We introduce a function space that serves as a trace space for nonlocal Dirichlet problems ...