Semigroups generated by elliptic operators in non-divergence form on C-o(Ω)

• Wolfgang Arendt ^[1] ; Reiner Michael Schätzle ^[2]
  1. [1] University of Ulm

     University of Ulm

     Stadtkreis Ulm, Alemania

     
  2. [2] Eberhard-Karls-University of Tübingen, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 2, 2014, págs. 417-434
• Idioma: inglés
• Enlaces
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• Resumen

  • Let  ⇢ Rn be a bounded open set satisfying the uniform exterior cone condition. Let A be a uniformly elliptic operator given by Au = Xn i, j=1 ai j @i j u + Xn j=1 b j @ j u + cu where a j i = ai j 2 C(¯ ) and b j , c 2 L1(), c  0 .

    We show that the realization A0 of A in C0() := {u 2 C(¯ ) : u|@ = 0} given by D(A0) := {u 2 C0() \ W2,n loc () : Au 2 C0()} A0u := Au generates a bounded holomorphic C0-semigroup on C0(). The result is in particular true if  is a Lipschitz domain. So far the best known result seems to be the case where  has C2-boundary [12, Section 3.1.5]. We also study the elliptic problem −Au = f u|@ = g .