Abstract:
A notion of almost minimizers is introduced for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli–Silvestre extension. In particular, almost fractional harmonic functions and almost minimizers for the fractional obstacle problem with zero obstacle are treated. It is shown that for a certain range of parameters, almost minimizers are almost Lipschitz or C1,β-regular.
Keywords:
almost minimizers, fractional Laplacian, fractional harmonic functions, fractional obstacle problem, regularity of solutions.
Citation:
S. Jeon, A. Petrosyan, “Almost minimizers for certain fractional variational problems”, Algebra i Analiz, 32:4 (2020), 166–199; St. Petersburg Math. J., 32:4 (2021), 729–751
\Bibitem{JeoPet20}
\by S.~Jeon, A.~Petrosyan
\paper Almost minimizers for certain fractional variational problems
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 4
\pages 166--199
\mathnet{http://mi.mathnet.ru/aa1715}
\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 4
\pages 729--751
\crossref{https://doi.org/10.1090/spmj/1667}
Linking options:
https://www.mathnet.ru/eng/aa1715
https://www.mathnet.ru/eng/aa/v32/i4/p166
This publication is cited in the following 2 articles:
Agnid Banerjee, Nicola Garofalo, “On the space-like analyticity in the extension problem for nonlocal parabolic equations”, Proc. Amer. Math. Soc., 151:3 (2022), 1235
S. Jeon, A. Petrosyan, “Almost minimizers for the thin obstacle problem”, Calc. Var. Partial Differ. Equ., 60:4 (2021), 124
Citation in format AMSBIB
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