Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy

We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at least one viscosity solution of class C l o c 1 , α , for some constant α ∈ ( 0 , 1 ) . In addition, under suitable cond...

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Veröffentlicht in:	Nonlinearity 2024-04, Vol.37 (4), p.45009
Hauptverfasser:	Andrade, Pêdra D S, dos Prazeres, Disson S, Santos, Makson S
Format:	Artikel
Sprache:	eng
Schlagworte:	35B65 35D40 35R09 35R11 degenerate operators Hölder regularity nonlocal operators singular operators
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creator	Andrade, Pêdra D S dos Prazeres, Disson S Santos, Makson S
description	We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at least one viscosity solution of class C l o c 1 , α , for some constant α ∈ ( 0 , 1 ) . In addition, under suitable conditions on degree of the operator σ , we prove regularity estimates in Hölder spaces for any viscosity solution. We also examine the singular setting and prove Hölder regularity estimates for the gradient of the solutions.
doi_str_mv	10.1088/1361-6544/ad2c22
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subjects	35B65 35D40 35R09 35R11 degenerate operators Hölder regularity nonlocal operators singular operators
title	Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy
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