Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group

2022/07/08 by Manfredini, Maria, Palatucci, Giampiero, Piccinini, Mirco +1 · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.03741

Abstract

We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian operator on the Heisenberg-Weyl group ℍⁿ. Amongst other results, we prove that the weak solutions to such a class of problems are bounded and Hölder continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates.

Cited by

• Fractional Morrey-Sobolev type embeddings and nonlocal subelliptic problems with oscillating nonlinearities on stratified Lie groups
• Brezis-Nirenberg type problem for fractional sub-Laplacian on the Heisenberg group
• Regularity for Mixed Local and Nonlocal Degenerate Elliptic Equations in the Heisenberg Group
• Fujita exponent for the fractional sub-Laplace semilinear heat equation with forcing term on the Heisenberg group

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