On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. I
The authors 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 \(a,b,c,V\). They use the associated sesquilinear form \(\tau\) and give a general method of constructing positive \(C_0\)-semigroups on \(L_p\) corresponding to a not necessarily sectorial form \(t\) on \(L_2\). Their approach is based upon approximations by sectorial forms where the potential is approximated. The procedure is realized by the use of the perturbation theory of positive operators. [For Part II, see the following review)].
\(L_p\) properties of second-order elliptic differential operators
perturbation theory of positive operators
scientific article; zbMATH DE number 1836671
scientific article