Geodesic
Weighted estimates of a~solution to the linear problem connected with one-phase Stefan problem in the case of the specific heat tends to zero
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 239-263

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We prove estimates in weighted Hölder norms for a solution to the model linear problem related with the one-phase Stefan problem with a small multiplier $\varepsilon$ at time derivative in the heat equation. These estimates are uniform with respect to parameter $\varepsilon$ and will be significant in the justification of passage to the limit in the one-phase Stefan problem with the specific heat tends to zero. 
@article{ZNSL_2006_336_a10,
     author = {V. A. Solonnikov and E. V. Frolova},
     title = {Weighted estimates of a~solution to the linear problem connected with one-phase {Stefan} problem in the case of the specific heat tends to zero},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {239--263},
     publisher = {mathdoc},
     volume = {336},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_336_a10/}
}
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V. A. Solonnikov; E. V. Frolova. Weighted estimates of a~solution to the linear problem connected with one-phase Stefan problem in the case of the specific heat tends to zero. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 239-263. http://geodesic.mathdoc.fr/item/ZNSL_2006_336_a10/