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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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v264_n12_p7270_daSilva http://hdl.handle.net/20.500.12110/paper_00220396_v264_n12_p7270_daSilva |
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| Sumario: | 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. |
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