Geodesic
Elliptic regularization of some semilinear parabolic free boundary problems
Alessandro Audrito1 orcid ; Tomás Sanz-Perela2 orcid
1Politecnico di Torino, Italy
2Universidad Autónoma de Madrid, Spain
Interfaces and free boundaries, Tome 26 (2024) no. 1, pp. 135-159

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DOI

We prove the existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. The Existence of solutions is obtained in two steps: we first show some uniform energy estimates and then we pass to the weak limit. To carry out the latter step, we establish uniform non-degeneracy estimates for the approximating sequence as well as parabolic non-degeneracy and optimal regularity for the limit solution. To the best of our knowledge, this is the first time the elliptic regularization approach is used in the context of parabolic obstacle problems.
DOI : 10.4171/ifb/511
Classification : 35-XX
Mots-clés : elliptic regularization, uniform estimates, variational techniques, non-degeneracy

Alessandro Audrito  1   ; Tomás Sanz-Perela  2

1 Politecnico di Torino, Italy
2 Universidad Autónoma de Madrid, Spain 
Alessandro Audrito; Tomás Sanz-Perela. Elliptic regularization of some semilinear parabolic free boundary problems. Interfaces and free boundaries, Tome 26 (2024) no. 1, pp. 135-159. doi: 10.4171/ifb/511
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     title = {Elliptic regularization of some semilinear parabolic free boundary problems},
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     pages = {135--159},
     year = {2024},
     volume = {26},
     number = {1},
     doi = {10.4171/ifb/511},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/511/}
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