Mathematics

Dr. Karthik Adimurthi
Seoul National University, South Korea

In this talk, extending the pioneering work of Juha Kinnunen and John Lewis, we will discuss the higher integrability for very weak solutions of quasilinear parabolic PDE with both constant and variable exponent growth. In the variable exponent problem, there is a genuine difficulty which arises due the the nature of intrinsic scaling which is different in the singular case and degenerate case. In joint work with Sun-Sig Byun and Jehan Oh, we develop the method of unified intrinsic scaling which enables us handle both the singular case and degenerate case simultaneously. This unified intrinsic scaling gives some very interesting improvements over many estimates available in current literature.