Positive weak supersolutions of the fractional a-Laplacian have positive linear boundary growth (a Hopf-type lower bound) under interior ball and growth conditions.
Boundary behavior of solutions to fractional $p$-Laplacian equation
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abstract
In this work, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for solutions to fractional $p$-Laplacian equations. Then, the isolation of the first $(s,p)$-eigenvalue is shown in bounded open sets satisfying the Wiener criterion.
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2024 1verdicts
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Hopf's lemmas and boundary behaviour of solutions to the fractional Laplacian in Orlicz-Sobolev spaces
Positive weak supersolutions of the fractional a-Laplacian have positive linear boundary growth (a Hopf-type lower bound) under interior ball and growth conditions.