Abstract
© 2019 Walter de Gruyter GmbH, Berlin/Boston 2019. We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., divA(x, Du) = div F, when A is a p-harmonic type operator, and under the assumption that x → A(x, ζ) belongs to the critical Besov-Lipschitz space B an/a,q∗ We prove that some fractional differentiability assumptions on F transfer to Du with no losses in the natural exponent of integrability. When div F = 0, we show that an analogous extra differentiability property for Du holds true under a Triebel- Lizorkin assumption on the partial map x → A(x, ζ).
Original language | English |
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Pages (from-to) | 762-778 |
Journal | Advances in Nonlinear Analysis |
Volume | 8 |
DOIs | |
Publication status | Published - 1 Jan 2019 |
Keywords
- Besov spaces
- Nonlinear elliptic equations
- Triebel-Lizorkin spaces
- higher order fractional differentiability
- p-harmonic operators