We establish Calder\'on \& Zygmund type estimates for a class of parabolic problems whose model is the non-homogeneous, degenerate/singular parabolic $p$-Laplacan system $$u_t - div \ (|Du|^{p-2}Du) = div \ (|F|^{p-2}F)\;, $$ proving that $$ F \in L_{\loc} ^{ q} \Longrightarrow Du\in L^{q}_{\loc} \qquad \forall \ q\geq p\;.$$ We also treat systems with discontinuous coefficients of vanishing mean oscillation (VMO) type.

Gradient estimates for a class of parabolic systems / Acerbi, Emilio Daniele Giovanni; Mingione, Giuseppe. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 136:(2007), pp. 285-320.

Gradient estimates for a class of parabolic systems

ACERBI, Emilio Daniele Giovanni;MINGIONE, Giuseppe
2007-01-01

Abstract

We establish Calder\'on \& Zygmund type estimates for a class of parabolic problems whose model is the non-homogeneous, degenerate/singular parabolic $p$-Laplacan system $$u_t - div \ (|Du|^{p-2}Du) = div \ (|F|^{p-2}F)\;, $$ proving that $$ F \in L_{\loc} ^{ q} \Longrightarrow Du\in L^{q}_{\loc} \qquad \forall \ q\geq p\;.$$ We also treat systems with discontinuous coefficients of vanishing mean oscillation (VMO) type.
2007
Gradient estimates for a class of parabolic systems / Acerbi, Emilio Daniele Giovanni; Mingione, Giuseppe. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 136:(2007), pp. 285-320.
File in questo prodotto:
File Dimensione Formato  
AMDuke07.pdf

non disponibili

Tipologia: Documento in Post-print
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 366.11 kB
Formato Adobe PDF
366.11 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1493301
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 368
  • ???jsp.display-item.citation.isi??? 365
social impact