On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. II
[For Part I, see the preceding review)]. The authors continue to study the \(L_p\) properties of second-order elliptic differential operators corresponding to expressions \(\Lambda=-\nabla.(a\nabla) + b.\nabla+ \nabla.c+V\) with singular measurable coefficients \(a,b,c,V\). Here, they consider the case of uniformly elliptic operators. They obtain the interval \((p_{\min}, p_{\max})\) in the \(L_p\)-scale, where the associated quasi-contractive \(C_0\)-semigroups can be defined on \(L_p\) spaces. The Sharpness of the main result is proven and the analyticity of the generators are given for \(p\) where the semigroup is defined.
\(L_p\) properties of second-order elliptic differential operators
scientific article; zbMATH DE number 1836672
scientific article