LINEAR PARABOLIC EQUATIONS IN LOCALLY UNIFORM SPACES
José M. Arrieta, Anı́bal Rodriguez-Bernal, Jan W. Cholewa, Tomasz W. Dłotko · Mathematical Models and Methods in Applied Sciences · 2004
We analyze the linear theory of parabolic equations in uniform spaces. We obtain sharp Lp-Lq-type estimates in uniform spaces for heat and Schrödinger semigroups and analyze the regularizing effect and the exponential type of these semigroups. We also deal with general second-order elliptic operators and study the generation of analytic semigoups in uniform spaces.