The nonstationary Venttsel' problem with quadratic growth with respect to the gradient
In our paper [Algebra Anal. 6, No. 6, 1-29 (1994; Zbl 0839.35061); Engl. translation: St. Petersbg. Math. J. 6, No. 6, 1127-1149 (1995)], a priori estimates for the gradient of a solution to an initial boundary value problem for the parabolic equation with weakly nonlinear Venttsel' boundary condition were established and the solvability of this problem was proved. In this paper, we consider the Venttsel' problem in the case where the right-hand sides of the equation and the boundary condition are of quadratic growth with respect to the gradient. Summable singularities in independent variables are also admitted. This requires the derivation of Hölder estimates with a large exponent with respect to the variable \(t\).
scientific article; zbMATH DE number 993656