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

Wolfgang Arendt, Reiner Schätzle
2014 Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V  
Let ⇢ R n be a bounded open set satisfying the uniform exterior cone condition. Let A be a uniformly elliptic operator given by generates a bounded holomorphic C 0 -semigroup on C 0 (). The result is in particular true if is a Lipschitz domain. So far the best known result seems to be the case where has C 2 -boundary [12, Section 3.1.5]. We also study the elliptic problem Mathematics Subject Classification (2010): 35K20 (primary); 35J25, 47D06 (secondary).
doi:10.2422/2036-2145.201111_010 fatcat:5m2sptdfczdkri2obqycamil5y