6533b85afe1ef96bd12b961d

RESEARCH PRODUCT

Improved Hölder regularity for strongly elliptic PDEs

Aleksis KoskiJarmo JääskeläinenAlbert ClopKari AstalaDaniel FaracoDaniel Faraco

subject

Hölder regularityGeneral MathematicsMathematics::Analysis of PDEsElliptic pdes01 natural sciencesBeltrami equationMathematics - Analysis of PDEsFOS: Mathematics0101 mathematicsComplex Variables (math.CV)Divergence (statistics)MathematicsDegree (graph theory)Mathematics - Complex VariablesPlane (geometry)Applied Mathematics010102 general mathematicsMathematical analysisQuasiconformal mappingsElliptic equations30C62 (Primary) 35J60 35B65 (Secondary)010101 applied mathematicsNonlinear systemType equationBeltrami equationExponentAnalysis of PDEs (math.AP)

description

We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of H\"older regularity, higher than what is given by the classical exponent $1/K$.

yearjournalcountryeditionlanguage
2019-06-26
10.1016/j.matpur.2020.06.005https://aaltodoc.aalto.fi/handle/123456789/61827