In this note we collect some pointwise bounds for the gradient of solutions, and for the solutions themselves, to the p-Laplace system with right-hand side in divergence form. Both estimates inside the domain for local solutions, and global estimates for solutions to boundary value problems are discussed. Their formulation involves sharp maximal operators, whose properties enable us to translate some aspects of the elliptic regularity theory into a merely harmonic-analytic framework. As a consequence, a flexible, comprehensive approach to estimates for solutions th p-Laplace system for a broad class of norms is derived. In particular, global estimates under minimal boundary regularity are presented.

The p-Laplace system with right-hand side in divergence form: Inner and up to the boundary pointwise estimates / Breit, D.; Cianchi, Andrea; Diening, L.; Kuusi, T.; Schwarzacher, S.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 153(2017), pp. 200-212. [10.1016/j.na.2016.06.011]

The p-Laplace system with right-hand side in divergence form: Inner and up to the boundary pointwise estimates

CIANCHI, ANDREA;
2017

Abstract

In this note we collect some pointwise bounds for the gradient of solutions, and for the solutions themselves, to the p-Laplace system with right-hand side in divergence form. Both estimates inside the domain for local solutions, and global estimates for solutions to boundary value problems are discussed. Their formulation involves sharp maximal operators, whose properties enable us to translate some aspects of the elliptic regularity theory into a merely harmonic-analytic framework. As a consequence, a flexible, comprehensive approach to estimates for solutions th p-Laplace system for a broad class of norms is derived. In particular, global estimates under minimal boundary regularity are presented.
153
200
212
Breit, D.; Cianchi, Andrea; Diening, L.; Kuusi, T.; Schwarzacher, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/1101576
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