6533b82dfe1ef96bd1290abb

RESEARCH PRODUCT

Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian

Mikko ParviainenAmal Attouchi

subject

viscosity solutionsApplied MathematicsGeneral Mathematicsta111010102 general mathematicsMathematical analysisparabolic01 natural sciencesNoise (electronics)non-homogeneouslocal C-alpha regularityTerm (time)010101 applied mathematicsViscosityBounded functionNon homogeneousEvolution equationp-Laplacian0101 mathematicsnormalized p-LaplacianFlatness (mathematics)Mathematics

description

In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.

yearjournalcountryeditionlanguage
2018-05-20Communications in Contemporary Mathematics
https://doi.org/10.1142/s0219199717500353