The nonstationary Venttsel' problem with quadratic growth with respect to the gradient
type: Item
instance of: scholarly article
title: The nonstationary Venttsel' problem with quadratic growth with respect to the gradient
zbMATH Open document ID: 0867.35048
DOI: 10.1007/BF02362382
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-03-23T00:00:00Z
review text: 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 \(t\).
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 993656
zbMATH Keywords: a priori estimates for the gradient
zbMATH Keywords: Hölder estimates
author: Darya E. Apushkinskaya
author: A. I. Nazarov
MaRDI profile type: Publication
cites work: Q4840963
cites work: On the quasilinear stationary Venttsel boundary value problem
cites work: Convex-monotone hulls and an estimate of the maximum of the solution of a parabolic equation
cites work: A survey of results on the solubility of boundary-value problems for second-order uniformly elliptic and parabolic quasi-linear equations having unbounded singularities
cites work: Q4853573
cites work: Boundary estimates for the first-order derivatives of a solution to a nondivergent parabolic equation with composite right-hand side and coefficients of lower-order derivatives
full work available at URL: https://doi.org/10.1007/bf02362382
OpenAlex ID: W2064024608
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description: scientific article; zbMATH DE number 993656