A One-Dimensional Parabolic Problem Arising in Studies of Some Free Boundary Problems.

The paper is concerned with a one-dimensional parabolic problem in a domain bounded by two lines x = 0 and x = kt, k > 0, (x, t) ∈ <MATH>\Bbb R^2</MATH>, with the Neumann boundary condition on the line x = 0 and with dynamic boundary condition on the line x = kt. For the solution of this problem, a coercive estimate in a weighted Hölder norm is obtained. It is shown that this estimate can be useful for the analysis of parabolic free boundary problems. Bibliography: 7 titles. [ABSTRACT FROM AUTHOR]