The regularity of generalized solutions for the n-dimensional quasi-linear parabolic diffraction problems Original Research Article

In this paper, we study the regularity of generalized solutions u(x,t)u(x,t) for the n-dimensional quasi-linear parabolic diffraction problem. By using various estimates and Steklov average methods, we prove that (1): for almost all tt the first derivatives ux(x,t)ux(x,t) are Hölder continuous with respect to xx up to the inner boundary, on which the coefficients of the equation are allowed to be discontinuous; and (2): the first derivative ut(x,t)ut(x,t) is Hölder continuous with respect to (x,t)(x,t) across the inner boundary.