Tug-of-War games and parabolic problems with spatial and time dependence
In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form {K(x,t)(Du)ut(x,t)=12⟨D2uJ(x,t)(Du),J(x,t)(Du)(x,t)⟩u(x,t)=F(x)in ΩT,on Γ, where ΩT=Ω×(0,T]ΩT=Ω×(0,T] and ΓΓ is its parabolic boundary. This problem can be vi...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2014 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/33121 |
| Online Access: | http://hdl.handle.net/11336/33121 |
| Access Level: | Open access |
| Keyword: | Tug-Of-War Parabolic https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form {K(x,t)(Du)ut(x,t)=12⟨D2uJ(x,t)(Du),J(x,t)(Du)(x,t)⟩u(x,t)=F(x)in ΩT,on Γ, where ΩT=Ω×(0,T]ΩT=Ω×(0,T] and ΓΓ is its parabolic boundary. This problem can be viewed as a version with spatial and time dependence of the evolution problem given by the infinity Laplacian, ut(x,t)=⟨D2u(x,t)Du|Du|(x,t),Du|Du|(x,t)⟩. |
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