Besov regularity for solutions of p-harmonic equations
By A. Clop, Raffaella Giova, Antonia Passarelli di Napoli. 2017
48 citations recorded by the source corpus.
Abstract We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., div 𝒜 ( x , D u ) = div F , {\operatorname{div}\mathcal{A}(x,Du)=\operatorname{div}F,} when 𝒜 {\mathcal{A}} is a p-harmonic type operator, and under the assumption that x ↦ 𝒜 ( x , ξ ) {x\mapsto\mathcal{A}(x,\xi\/)} belongs to the critical Besov–Lipschitz space B n / α , q α {B^{\alpha}_{{n/\alpha},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 {\operatorname{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 , ξ ) {x\mapsto\mathcal{A}(x,\xi\/)} .
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c37e81bc385df95ca1d87d604eea918a1d10b687
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In Applied Mathematics
- Michela Eleuteri
- Antonia Passarelli di Napoli
- P. Hasto
- Giuseppe Mingione
- Paolo Marcellini
- Raffaella Giova
- Jihoon Ok
In Mathematical Physics
Citations in the corpus
- Higher differentiability for solutions to a class of obstacle problems (2018, background): “4) show that the weak differentiability of integer or fractional order of the map A, as function of the x-variable, is a sufficient condition (see [24,25,40–42] for the case of Sobolev space with integer order and [2,15] for the fractional one).”