Regularity for degenerate evolution equations with strong absorption
In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2≤p<∞) under a strong absorption condition: Δpu−[Formula presented]=λ0u+ qinΩT:=Ω×(0,T), where 0≤q<1. This model is interesting because it yields the formation of dead-co...
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todo:paper_00220396_v264_n12_p7270_daSilva2023-10-03T14:25:37Z Regularity for degenerate evolution equations with strong absorption da Silva, J.V. Ochoa, P. Silva, A. Dead-core problems Liouville type results p-Laplacian type operators Sharp and improved intrinsic regularity In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2≤p<∞) under a strong absorption condition: Δpu−[Formula presented]=λ0u+ qinΩT:=Ω×(0,T), where 0≤q<1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u,ΩT)=∂{u>0}∩ΩT (the free boundary), where α=[Formula presented]≥1+[Formula presented]. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator. © 2018 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00220396_v264_n12_p7270_daSilva |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Dead-core problems Liouville type results p-Laplacian type operators Sharp and improved intrinsic regularity |
| spellingShingle |
Dead-core problems Liouville type results p-Laplacian type operators Sharp and improved intrinsic regularity da Silva, J.V. Ochoa, P. Silva, A. Regularity for degenerate evolution equations with strong absorption |
| topic_facet |
Dead-core problems Liouville type results p-Laplacian type operators Sharp and improved intrinsic regularity |
| description |
In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2≤p<∞) under a strong absorption condition: Δpu−[Formula presented]=λ0u+ qinΩT:=Ω×(0,T), where 0≤q<1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u,ΩT)=∂{u>0}∩ΩT (the free boundary), where α=[Formula presented]≥1+[Formula presented]. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator. © 2018 Elsevier Inc. |
| format |
JOUR |
| author |
da Silva, J.V. Ochoa, P. Silva, A. |
| author_facet |
da Silva, J.V. Ochoa, P. Silva, A. |
| author_sort |
da Silva, J.V. |
| title |
Regularity for degenerate evolution equations with strong absorption |
| title_short |
Regularity for degenerate evolution equations with strong absorption |
| title_full |
Regularity for degenerate evolution equations with strong absorption |
| title_fullStr |
Regularity for degenerate evolution equations with strong absorption |
| title_full_unstemmed |
Regularity for degenerate evolution equations with strong absorption |
| title_sort |
regularity for degenerate evolution equations with strong absorption |
| url |
http://hdl.handle.net/20.500.12110/paper_00220396_v264_n12_p7270_daSilva |
| work_keys_str_mv |
AT dasilvajv regularityfordegenerateevolutionequationswithstrongabsorption AT ochoap regularityfordegenerateevolutionequationswithstrongabsorption AT silvaa regularityfordegenerateevolutionequationswithstrongabsorption |
| _version_ |
1782025679634694144 |