Optimal second-order regularity in the space variables is established for solutions to Cauchy–Dirichlet problems for nonlinear parabolic equations and systems of p-Laplacian type, with square-integrable right-hand sides and initial data in a Sobolev space. As a consequence, generalized solutions are shown to be strong solutions. Minimal regularity on the boundary of the domain is required, though the results are new even for smooth domains. In particular, they hold in arbitrary bounded convex domains.
Second-Order Regularity for Parabolic p-Laplace Problems / Cianchi A.; Maz'ya V.G.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 30:(2020), pp. 1565-1583. [10.1007/s12220-019-00213-3]
Second-Order Regularity for Parabolic p-Laplace Problems
Cianchi A.
;
2020
Abstract
Optimal second-order regularity in the space variables is established for solutions to Cauchy–Dirichlet problems for nonlinear parabolic equations and systems of p-Laplacian type, with square-integrable right-hand sides and initial data in a Sobolev space. As a consequence, generalized solutions are shown to be strong solutions. Minimal regularity on the boundary of the domain is required, though the results are new even for smooth domains. In particular, they hold in arbitrary bounded convex domains.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.