A Hopf's lemma and the boundary regularity for the fractional p-Laplacian
Copyright policy )A Hopf's lemma and the boundary regularity for the fractional p-Laplacian
We begin the paper with a Hopf's lemma for a fractional p-Laplacian problem on a half-space. Specifically speaking, we show that the derivative of the solution along the outward normal vector is strictly positive on the boundary of the half-space. Next we show that positive solutions to a fractional p-Laplacian equation possess certain Holder continuity up to the boundary.
- Baylor University United States
Smoothness and regularity of solutions to PDEs, Positive solutions to PDEs, Pseudodifferential operators as generalizations of partial differential operators, Fractional partial differential equations, Maximum principles in context of PDEs, boundary regularity, Mathematics - Analysis of PDEs, fractional \(p\)-Laplacian, Hopf's lemma, FOS: Mathematics, Dirichlet problem, Analysis of PDEs (math.AP)
Smoothness and regularity of solutions to PDEs, Positive solutions to PDEs, Pseudodifferential operators as generalizations of partial differential operators, Fractional partial differential equations, Maximum principles in context of PDEs, boundary regularity, Mathematics - Analysis of PDEs, fractional \(p\)-Laplacian, Hopf's lemma, FOS: Mathematics, Dirichlet problem, Analysis of PDEs (math.AP)
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