Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains
Let \(E\) be a locally compact separable metric space and let \(m\) be a positive finite measure on \(E\) with support equal to \(E\). The authors extend first the concept of intrinsic ultracontractivity to non-symmetric absolutely continuous semigroups acting on \(L^2(E,m)\). Moreover, some applications of this notion are given. Then, they prove essentially that, the Dirichlet semigroups of non-symmetric second order elliptic operators in bounded Lipschitz domains of \(\mathbb{R}^d\), are intrinsic ultracontractive. To do this, they use as a bridge, the (symmetric) semigroup defined by the symmetric part of the initial Dirichlet form. Then they use the logarithmic Sobolev inequalities.
scientific article; zbMATH DE number 5528029
scientific article