Higher integrability for nonlinear nonlocal equations with irregular kernel

Nowak SN (2021)
In: Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs. Grigor’yan A, Sun Y (Eds); Advances in analysis and geometry, 3. Berlin: De Gruyter: 459-492.

Sammelwerksbeitrag | Veröffentlicht | Englisch
 
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Herausgeber*in
Grigor’yan, Alexander; Sun, Yuhua
Abstract / Bemerkung
We prove a higher regularity result for weak solutions to nonlinear nonlocal equations along the integrability scale of Bessel potential spaces Hs,p under a mild continuity assumption on the kernel. By embedding, this also yields regularity in Sobolev-Slobodeckij spaces Ws,p. Our approach is based on a characterization of Bessel potential spaces in terms of a certain nonlocal gradient-type operator and a perturbation approach commonly used in the context of local elliptic equations in divergence form.
Erscheinungsjahr
2021
Buchtitel
Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
Serientitel
Advances in analysis and geometry
Band
3
Seite(n)
459-492
eISBN
978-3-11-070076-3
Page URI
https://pub.uni-bielefeld.de/record/2962555

Zitieren

Nowak SN. Higher integrability for nonlinear nonlocal equations with irregular kernel. In: Grigor’yan A, Sun Y, eds. Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs. Advances in analysis and geometry. Vol 3. Berlin: De Gruyter; 2021: 459-492.
Nowak, S. N. (2021). Higher integrability for nonlinear nonlocal equations with irregular kernel. In A. Grigor’yan & Y. Sun (Eds.), Advances in analysis and geometry: Vol. 3. Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs (pp. 459-492). Berlin: De Gruyter. https://doi.org/10.1515/9783110700763-017
Nowak, S. N. (2021). “Higher integrability for nonlinear nonlocal equations with irregular kernel” in Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs, Grigor’yan, A., and Sun, Y. eds. Advances in analysis and geometry, vol. 3, (Berlin: De Gruyter), 459-492.
Nowak, S.N., 2021. Higher integrability for nonlinear nonlocal equations with irregular kernel. In A. Grigor’yan & Y. Sun, eds. Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs. Advances in analysis and geometry. no.3 Berlin: De Gruyter, pp. 459-492.
S.N. Nowak, “Higher integrability for nonlinear nonlocal equations with irregular kernel”, Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs, A. Grigor’yan and Y. Sun, eds., Advances in analysis and geometry, vol. 3, Berlin: De Gruyter, 2021, pp.459-492.
Nowak, S.N.: Higher integrability for nonlinear nonlocal equations with irregular kernel. In: Grigor’yan, A. and Sun, Y. (eds.) Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs. Advances in analysis and geometry. 3, p. 459-492. De Gruyter, Berlin (2021).
Nowak, Simon Noah. “Higher integrability for nonlinear nonlocal equations with irregular kernel”. Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs. Ed. Alexander Grigor’yan and Yuhua Sun. Berlin: De Gruyter, 2021.Vol. 3. Advances in analysis and geometry. 459-492.

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