Global regularity for a class of fully nonlinear PDEs with unbalanced variable degeneracy

Silva, João Vítor da; Júnior, Elzon C. B.; Rampasso, Giane C.; Ricarte, Gleydson C.

doi:10.48550/arxiv.2108.08343

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2024

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“…with 0 < p ⩽ q were also investigated. We refer the reader to [21,24,28], and the references therein. The main novelty in those works is that equation ( 5) is no longer homogeneous, which makes the scaling process more delicate.…”

Section: Introductionmentioning

confidence: 99%

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

Andrade,

dos Prazeres,

Santos

2024

Nonlinearity

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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.

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Section: Introductionmentioning

confidence: 99%