Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
Motohiro Sobajima, Chiara Spina · Forum Mathematicum · 2015
Abstract We prove that, for N/(N-2) 2, the operator L u = (1 + |x|2)α/2Tr(A(x)D 2 u) = (1 + |x|2)α/2∑ i,j=1,...,N a ij (x)D ij u admits realizations generating analytic semigroups in Lp (ℝ N ). Moreover, for α < N/p', we provide an explicit description of the domain.