Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem
Volume 79 / 2002
Annales Polonici Mathematici 79 (2002), 207-232 MSC: 35J65, 35J70, 35B45. DOI: 10.4064/ap79-3-2
We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.