In this paper, we study two related features of the regularity of the weak solutions to a class of strongly degenerate parabolic equation i.e. the higher differentiability of a nonlinear function of the spatial gradient of the weak solutions, assuming only that f ∈ L2 loc (T ). This allows us to establish the higher integrability of the spatial gradient under the same minimal requirement on the datum f.
Higher regularity for weak solutions to degenerate parabolic problems / Gentile, Andrea; PASSARELLI DI NAPOLI, Antonia. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1432-0835. - 62:8(2023). [10.1007/s00526-023-02564-w]
Higher regularity for weak solutions to degenerate parabolic problems
Antonia Passarelli di Napoli
2023
Abstract
In this paper, we study two related features of the regularity of the weak solutions to a class of strongly degenerate parabolic equation i.e. the higher differentiability of a nonlinear function of the spatial gradient of the weak solutions, assuming only that f ∈ L2 loc (T ). This allows us to establish the higher integrability of the spatial gradient under the same minimal requirement on the datum f.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
