Abstract
We prove Hölder estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional p-Laplace equation
where \({s \in (0,1)}\) and \({p > 2}\) or \({1/(1-s) < p < 2}\). Our results also apply for inhomogeneous equations with more general kernels, when p and s are allowed to vary with x, without any regularity assumption on p and s. This complements and extends some of the recently obtained Hölder estimates for weak solutions.
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Supported by the Swedish Research Council, Grant No. 2012-3124. Partially supported by the Royal Swedish Academy of Sciences. A substantial part of this work was carried out at the Isaac Newton’s Institute, during the program “Free boundary problems” and I am thankful for the great hospitality.
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Lindgren, E. Hölder estimates for viscosity solutions of equations of fractional p-Laplace type. Nonlinear Differ. Equ. Appl. 23, 55 (2016). https://doi.org/10.1007/s00030-016-0406-x
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DOI: https://doi.org/10.1007/s00030-016-0406-x