Lp - Lq Estimates for parabolic systems in non-divergence form with VMO coefficients

Robert Haller-Dintelmann, Horst Heck, Matthias Georg Hieber

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Consider a parabolic N × N-system of order m on ℝn with top-order coefficients aα ∈ VMO∩L , Let 1 <p, q <∞ and let ω be a Muckenhoupt weight. It is proved that systems of this kind possess a unique solution u satisfying ||u′||Lq(J;Lωp(ℝn)N) + ||Au||Lq(J;Lωp,(ℝn)N) ≤ C||f|| Lq(J;Lωp(ℝn)N), where Au = Σ |α|≤maαDαu and J = [0, ∞ ). In particular, choosing ω = 1, the realization of A in L p(ℝn)N has maximal LpL q regularity.

Original languageEnglish
Pages (from-to)717-736
Number of pages20
JournalJournal of the London Mathematical Society
Issue number3
Publication statusPublished - 2006 Dec
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)

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