Regularity of Weak Solutions to a Class of Nonlinear Parabolic Equations in Fractional Sobolev Spaces (Contemporary Mathematics, 2024)
In this article, we study regularity of weak solutions to a class of nonlinear parabolic equations in divergence form. The main purpose is to present a regularity estimate with more general conditions on coefficients, N-functions and non-homogeneous terms in the fractional Sobolev spaces. By deriving a higher integrability estimate of weak solutions, we obtain the desired regularity estimate. In addition, the results of this article expand the regularity theory of parabolic equations in fractional Sobolev spaces and Besov spaces.
Keywords: nonlinear parabolic equations, regularity, fractional sobolev spaces