Higher regularity up to boundary for degenerate parabolic equations

In this paper, we study the degenerate parabolic equations of the form1+delta 1+delta ut =ai j uij+ 2xn ainuin + x1+delta 2 n annunn +biui + xn bnun + cu + f 2derived from the Constant Elasticity of Variance model in mathematical finance. Under certain smoothness conditions on coefficients and forcing term, the smoothness of solution for these problems is proved. Since the solution cannot be considered smooth with standard differentiability, we introduced a suitable weighted norm that makes the solution smooth. Using the weighted norm, we define the weighted Holder space Ck,2+alpha s and establish Schauder theory for Ck,2+alpha s regularity.(c) 2022 Elsevier Inc. All rights reserved.