We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part: near regular points the free boundary is C-8 in space and time. Furthermore, we prove that the set of singular points is locally covered by a Lipschitz manifold of dimension n - 1 which is also e-flat in space, for any e > 0.
Regularity theory for fully nonlinear parabolic obstacle problems / Audrito, A.; Kukuljan, T.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 285:10(2023). [10.1016/j.jfa.2023.110116]
Regularity theory for fully nonlinear parabolic obstacle problems
Audrito A.;
2023
Abstract
We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part: near regular points the free boundary is C-8 in space and time. Furthermore, we prove that the set of singular points is locally covered by a Lipschitz manifold of dimension n - 1 which is also e-flat in space, for any e > 0.File in questo prodotto:
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https://hdl.handle.net/11583/2985050