A pointwise bound for local weak solutions to the p-Laplace system is established in terms of data on the right-hand side in divergence form. The relevant bound involves a Havin-Maz'ya-Wolff potential of the datum. A local bound for oscillations is also provided. These results allow for a unified approach to regularity estimates for broad classes of norms, including Banach function norms (e.g. Lebesgue, Lorentz and Orlicz norms), and norms depending on the oscillation of functions (e.g. Hoelder, BMO and, more generally, Campanato type norms). In particular, new regularity properties are exhibited, and well-known results are easily recovered.
Potential estimates for the p-Laplace system with data in divergence form / Cianchi, A.*; Schwarzacher, S.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 265:(2018), pp. 478-499. [10.1016/j.jde.2018.02.038]
Potential estimates for the p-Laplace system with data in divergence form
Cianchi, A.
;
2018
Abstract
A pointwise bound for local weak solutions to the p-Laplace system is established in terms of data on the right-hand side in divergence form. The relevant bound involves a Havin-Maz'ya-Wolff potential of the datum. A local bound for oscillations is also provided. These results allow for a unified approach to regularity estimates for broad classes of norms, including Banach function norms (e.g. Lebesgue, Lorentz and Orlicz norms), and norms depending on the oscillation of functions (e.g. Hoelder, BMO and, more generally, Campanato type norms). In particular, new regularity properties are exhibited, and well-known results are easily recovered.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.