Geodesic
One-dimensional parabolic problem arising in the study of some free boundary problems
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 16, Tome 269 (2000), pp. 322-338

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The paper is concerned with one-dimensional parabolic problem in the domain bounded by straight lines $x=0$ and $x=kt$, $k>0$, $(x,t)\in\mathbb R^2$, with the Neumann boundary condition on the line $x=0$ and with dynamic boundary condition on the lne $x=kt$. For the solution of this problem 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. 
@article{ZNSL_2000_269_a21,
     author = {V. A. Solonnikov and A. Fasano},
     title = {One-dimensional parabolic problem arising in the study of some free boundary problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {322--338},
     publisher = {mathdoc},
     volume = {269},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a21/}
}
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V. A. Solonnikov; A. Fasano. One-dimensional parabolic problem arising in the study of some free boundary problems. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 16, Tome 269 (2000), pp. 322-338. http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a21/