Degenerate second order differential operators generating analytic semigroups in L^p and W^1,p

Authors

Angelo Favini, Alma Mater Studiorum Università di BolognaFollow
Giséle Ruiz Goldstein, University of MemphisFollow
Jerome A. Goldstein, University of MemphisFollow
Silvia Romanelli, Alma Mater Studiorum Università di Bologna

Abstract

We deal with the problem of analyticity for the semigroup generated by the second order differential operator Au:= αu″ + βu′ (or by some restrictions of it) in the spaces Lp(0, 1), with or without weight, and in W1,p(0, 1), 1 < p < ∞. Here α and β are assumed real-valued and continuous in [0, 1], with α(x) > 0 in (0, 1), and the domain of A is determined by the generalized Neumann boundary conditions and by Wentzell boundary conditions.

Publication Title

Mathematische Nachrichten

Recommended Citation

Favini, A., Goldstein, G., Goldstein, J., & Romanelli, S. (2002). Degenerate second order differential operators generating analytic semigroups in L^p and W^1,p. Mathematische Nachrichten, 238, 78-102. https://doi.org/10.1002/1522-2616(200205)238:1<78::AID-MANA78>3.0.CO;2-X