Higher-order elliptic and parabolic equations with VMO assumptions and general boundary conditions

Hongjie Dong, Chiara Gallarati

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

We prove mixed Lp(Lq)-estimates, with p,q∈(1,∞), for higher-order elliptic and parabolic equations on the half space R+ d+1 with general boundary conditions which satisfy the Lopatinskii–Shapiro condition. We assume that the elliptic operators A have leading coefficients which are in the class of vanishing mean oscillations both in the time variable and the space variable. In the proof, we apply and extend the techniques developed by Krylov [24] as well as Dong and Kim in [13] to produce mean oscillation estimates for equations on the half space with general boundary conditions.

Original languageEnglish
Pages (from-to)1993-2038
Number of pages46
JournalJournal of Functional Analysis
Volume274
Issue number7
DOIs
Publication statusPublished - 2018

Keywords

  • Inhomogeneous boundary conditions
  • Mixed-norms
  • Muckenhoupt weights
  • The Lopatinskii–Shapiro condition

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