Global H\"older regularity for the fractional $p$-Laplacian

By Antonio Iannizzotto, Sunra Mosconi, Marco Squassina. 2014

286 citations recorded by the source corpus.

By virtue of barrier arguments we prove $C^\alpha$-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ($p 2$) case.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/704065efce5eca10b2b0c5c301fa04b2d91b2f16

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Existence results for fractional p-Laplacian problems via Morse theory (2014, background): “How to achieve (RC) in the nonlinear case p ̸ = 2 is still an open problem, yet a partial result in this direction (namely, Cá-regularity up to the boundary of the weak solutions) is provided in the forthcoming paper [20].”
Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations (2016, background): “Also, we would like to mention the related results involving measure data, as seen in [1, 23, 26], and the fine analysis in the papers [3, 12, 24, 25, 28] where various results for fractional p-eigenvalues have been proven.”
Nonlocal problems with critical Hardy nonlinearity (2017, background): “Finally, the regularity up to the boundary is proven in [12] (notice that we are assuming 0 / ∈ ∂Ω).”
Linear theory for a mixed operator with Neumann conditions (2020, unknown): “We combine for this proof some classical and nonlocal techniques, see e.g. [34, 35,43,45,46,53,54].”
Bifurcation and multiplicity results for critical fractional p‐Laplacian problems (2014, background): “ Palatucci [20], Iannizzotto and Squassina [28] and in Lindgren and Lindqvist [31]. Regularity of solutions was obtained in Di Castro, Kuusi and Palatucci [14, 15], Iannizzotto, Mosconi and Squassina [26], Kuusi, Mingione and Sire [29] and Lindgren [30]. Existence via Morse theory was investigated i”
Fractional double-phase patterns: concentration and multiplicity of solutions (2020, methodology): “3 in [48], we can prove that the above definitions make sense.”