WEIGHTED ESTIMATES OF A SOLUTION TO THE LINEAR PROBLEM CONNECTED WITH THE ONE-PHASE STEFAN PROBLEM IN THE CASE WHERE THE SPECIFIC HEAT TENDS TO ZERO

摘要

We prove estimates in weighted Hoelder norms for a solution to the model linear problem related with the one-phase Stefan problem with a small multiplier ε at time derivative in the heat equation. These estimates are uniform with respect to parameter ε and are significant in justification of passage to the limit in the one-phase Stefan problem as the specific heat tends to zero.