We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate for boundary singularities which are naturally built in the problem.
An elliptic boundary value problem with fractional nonlinearity / N. Abatangelo, M. Cozzi. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 53:3(2021 Jun 22), pp. 3577-3601. [10.1137/20M1342641]
An elliptic boundary value problem with fractional nonlinearity
M. Cozzi
2021
Abstract
We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate for boundary singularities which are naturally built in the problem.
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