Regularity results for weak solutions of elliptic PDEs below the natural exponent

Cruz-Uribe, David; Moen, Kabe; Rodney, Scott

doi:10.1007/s10231-015-0486-y

Regularity results for weak solutions of elliptic PDEs below the natural exponent

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Date

2016, 2016, 2016

Authors

Cruz-Uribe, David

Moen, Kabe

Rodney, Scott

Abstract

We prove regularity estimates for the weak solutions to the Dirichlet problem for a divergence form elliptic operator. We give estimates for the second derivative for . Our work generalizes results due to Miranda (Ann Mat Pura Appl 63(4):353-386, 1963).

Keywords

equations, inequalities, dirichlet problem, Elliptic PDEs, lipschitz-domains, potentials, Regularity, sobolev, spaces, theorem, vmo coefficients, w-1,w-p, Weak solutions, School of Science and Technology

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https://hdl.handle.net/20.500.14639/321

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Regularity results for weak solutions of elliptic PDEs below the natural exponent

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