Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 189, pp. 1-30.

Title: Generators with interior degeneracy on spaces of L^2 type
 
Authors: Genni Fragnelli  (Univ. di Bari "Aldo Moro", Bari, Italy)
         Gisele Ruiz Goldstein (Univ. of Memphis, TN, USA)
         Jerome A. Goldstein   (Univ. of Memphis, TN, USA)
	 Silvia Romanelli (Univ. di Bari "Aldo Moro", Bari, Italy)

Abstract:
 We consider operators in divergence and in nondivergence form with
 degeneracy at the interior of the space domain. Characterizing the
 domain of the operators, we prove that they generate positive
 analytic semigroups on spaces of L^2 type. Finally, some
 applications to linear and semilinear parabolic evolution problems
 and to linear hyperbolic ones are presented.

Submitted September 6, 2012. Published October 31, 2012.
Math Subject Classifications: 47D06, 35K65, 47B25, 47N20.
Key Words: Degenerate operators in divergence and non divergence form;
    linear and semiliner parabolic equations; linear hyperbolic equations.