Superdiffusion and parabolic nonlinear differential equations
The model under consideration is a \(d\)-dimensional superdiffusion \(X\) with parameters \((L,\alpha)\); that is, \(X\) is related to the parabolic differential equation \((\partial/\partial r)\nu+L\nu-|\nu|^ \alpha=-\rho\). Here \(1<\alpha\leq 2\), and \(L\) is a ``uniformly'' elliptic differential operator with bounded and sufficiently ``smooth'' coefficients (depending on time and space). Connections between \(X\) and that equation are established, especially concerning their minimal and maximal positive solutions. Analytic results are used to study the graph \({\mathcal G}\) of \(X\). In particular, a \({\mathcal G}\)-polar set is characterized as an analytic set of capacity 0 in the sense of \textit{N. G. Meyers} [Math. Scand. 26, 255-292 (1971; Zbl 0242.31006)].
scientific article; zbMATH DE number 89796