Maximal regularity result for a singular differential equation in the space of summable functions

Abstract

Abstract We give sufficient conditions for the unique solvability and maximal regularity of a generalized solution of a second-order differential equation with unbounded diffusion, drift, and potential coefficients. We prove the compactness of the resolvent of the equation and an upper bound for the Kolmogorov widths of the set of solutions. It is assumed that the intermediate coefficient grows quickly and does not depend on the growth of potential. The diffusion coefficient is positive and can grow or disappear near infinity, i.e. the equation under consideration can degenerate. The study of such equation is motivated by applications in stochastic processes and financial mathematics.