### Global Schauder estimates for the $p$-Laplace system

Breit D, Cianchi A, Diening L, Schwarzacher S (2019)
Archive for Rational Mechanics and Analysis .

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch

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Autor*in
Breit, Dominic; Cianchi, Andrea; Diening, LarsUniBi ; Schwarzacher, Sebastian
Einrichtung
Abstract / Bemerkung
An optimal first-order global regularity theory, in spaces of functions defined in terms of oscillations, is established for solutions to Dirichlet problems for the p-Laplace equation and system, with the right-hand side in divergence form. The exact mutual dependence among the regularity of the solution, of the datum on the right-hand side, and of the boundary of the domain in these spaces is exhibited. A comprehensive formulation of our results is given in terms of Campanato seminorms. New regularity results in customary function spaces, such as Holder, BMO and VMO spaces, follow as a consequence. Importantly, the conclusions are new even in the linear case when p = 2, and hence the differential operator is the plain Laplacian. Yet in this classical linear setting, our contribution completes and augments the celebrated Schauder theory in Holder spaces. A distinctive trait of our results is their sharpness, which is demonstrated by a family of apropos examples.
Erscheinungsjahr
2019
Zeitschriftentitel
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
eISSN
1432-0673
Page URI
https://pub.uni-bielefeld.de/record/2948397

### Zitieren

Breit D, Cianchi A, Diening L, Schwarzacher S. Global Schauder estimates for the $p$-Laplace system. Archive for Rational Mechanics and Analysis . 2019.
Breit, D., Cianchi, A., Diening, L., & Schwarzacher, S. (2019). Global Schauder estimates for the $p$-Laplace system. Archive for Rational Mechanics and Analysis . https://doi.org/10.1007/s00205-021-01712-w
Breit, D., Cianchi, A., Diening, L., and Schwarzacher, S. (2019). Global Schauder estimates for the $p$-Laplace system. Archive for Rational Mechanics and Analysis .
Breit, D., et al., 2019. Global Schauder estimates for the $p$-Laplace system. Archive for Rational Mechanics and Analysis .
D. Breit, et al., “Global Schauder estimates for the $p$-Laplace system”, Archive for Rational Mechanics and Analysis , 2019.
Breit, D., Cianchi, A., Diening, L., Schwarzacher, S.: Global Schauder estimates for the $p$-Laplace system. Archive for Rational Mechanics and Analysis . (2019).
Breit, Dominic, Cianchi, Andrea, Diening, Lars, and Schwarzacher, Sebastian. “Global Schauder estimates for the $p$-Laplace system”. Archive for Rational Mechanics and Analysis (2019).

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### Quellen

arXiv: 1903.12496