Higher order Calderon-Zygmund estimates for the p-Laplace equation

Khripunova Balci A, Diening L, Weimar M (2020)
JOURNAL OF DIFFERENTIAL EQUATIONS 268(2): 590-635.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck| Englisch
 
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Abstract / Bemerkung
The paper is concerned with higher order Calderon-Zygmund estimates for the p-Laplace equation div(A(del(u))) := - div (vertical bar del(u)vertical bar(p-2)del u) = -div F. 1 < p < infinity We are able to transfer local interior Besov and Triebel-Lizorkin regularity up to first order derivatives from the force term F to the flux A(del u). For p >= 2 we show that F is an element of B-Q,q(s) implies A(del u) is an element of B-Q,q(s) for any s is an element of (0, 1) and all reasonable Q, q is an element of (0, infinity] in the planar case. The result fails for p < 2. In case of higher dimensions and systems we have a smallness restriction on s. The quasi-Banach case 0 < min{Q, q} < 1 is included, since it has important applications in the adaptive finite element analysis. As an intermediate step we prove new linear decay estimates for p-harmonic functions in the plane for the full range 1 < p < infinity. (C) 2019 Elsevier Inc. All rights reserved.
Stichworte
p-Laplacian; Nonlinear elliptic equations; Regularity of solutions
Erscheinungsjahr
2020
Zeitschriftentitel
JOURNAL OF DIFFERENTIAL EQUATIONS
Band
268
Ausgabe
2
Seite(n)
590-635
ISSN
0022-0396
eISSN
1090-2732
Page URI
https://pub.uni-bielefeld.de/record/2938742

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Khripunova Balci A, Diening L, Weimar M. Higher order Calderon-Zygmund estimates for the p-Laplace equation. JOURNAL OF DIFFERENTIAL EQUATIONS. 2020;268(2):590-635.
Khripunova Balci, A., Diening, L., & Weimar, M. (2020). Higher order Calderon-Zygmund estimates for the p-Laplace equation. JOURNAL OF DIFFERENTIAL EQUATIONS, 268(2), 590-635. doi:10.1016/j.jde.2019.08.009
Khripunova Balci, A., Diening, L., and Weimar, M. (2020). Higher order Calderon-Zygmund estimates for the p-Laplace equation. JOURNAL OF DIFFERENTIAL EQUATIONS 268, 590-635.
Khripunova Balci, A., Diening, L., & Weimar, M., 2020. Higher order Calderon-Zygmund estimates for the p-Laplace equation. JOURNAL OF DIFFERENTIAL EQUATIONS, 268(2), p 590-635.
A. Khripunova Balci, L. Diening, and M. Weimar, “Higher order Calderon-Zygmund estimates for the p-Laplace equation”, JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 268, 2020, pp. 590-635.
Khripunova Balci, A., Diening, L., Weimar, M.: Higher order Calderon-Zygmund estimates for the p-Laplace equation. JOURNAL OF DIFFERENTIAL EQUATIONS. 268, 590-635 (2020).
Khripunova Balci, Anna, Diening, Lars, and Weimar, Markus. “Higher order Calderon-Zygmund estimates for the p-Laplace equation”. JOURNAL OF DIFFERENTIAL EQUATIONS 268.2 (2020): 590-635.