We prove a partial Hölder regularity result for weak solutions u : Ω → RN, N ≥ 2, to non-autonomous elliptic systems with general growth of the type - div a(x, u, Du) = b(x, u, Du) in Ω. The crucial point is that the operator a satisfies very weak regularity properties and general growth, while for the inhomogeneity b we allow a critical growth condition.
Partial regularity for elliptic systems with critical growth / Isernia, T.; Leone, C.; Verde, A.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 33:2(2022), pp. 271-296. [10.4171/RLM/971]
Partial regularity for elliptic systems with critical growth
Isernia T.
;
2022-01-01
Abstract
We prove a partial Hölder regularity result for weak solutions u : Ω → RN, N ≥ 2, to non-autonomous elliptic systems with general growth of the type - div a(x, u, Du) = b(x, u, Du) in Ω. The crucial point is that the operator a satisfies very weak regularity properties and general growth, while for the inhomogeneity b we allow a critical growth condition.File in questo prodotto:
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