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Annali di Matematica Pura ed Applicata

, Volume 191, Issue 2, pp 339–362 | Cite as

Global W 2, p estimates for nondivergence elliptic operators with potentials satisfying a reverse Hölder condition

  • M. BramantiEmail author
  • L. Brandolini
  • E. Harboure
  • B. Viviani
Article

Abstract

In this article, we give some a priori \({L^{p}(\mathbb{R}^{n})}\) estimates for elliptic operators in nondivergence form with VMO coefficients and a potential V satisfying an appropriate reverse Hölder condition, generalizing previous results due to Chiarenza–Frasca–Longo to the scope of Schrödinger-type operators. In particular, our class of potentials includes unbounded functions such as nonnegative polynomials. We apply such a priori estimates to derive some global existence and uniqueness results under some additional assumptions on V.

Keywords

Schrödinger operator Global existence and uniqueness Reverse Hölder condition VMO coefficients Global Lp estimates 

Mathematics Subject Classification (2000)

Primary 35J10 Secondary 35B45 35A05 42B35 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2011

Authors and Affiliations

  • M. Bramanti
    • 1
    Email author
  • L. Brandolini
    • 2
  • E. Harboure
    • 3
  • B. Viviani
    • 3
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Dipartimento di Ingegneria dell’Informazione e Metodi MatematiciUniversità degli Studi di BergamoDalmineItaly
  3. 3.Instituto de Matemática Aplicada del LitoralCONICET-Universidad Nacional del LitoralSanta FeRepublic of Argentina

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