Geodesic
An \(L^p\)-approach for the study of degenerate parabolic equations
Electronic journal of differential equations, Tome 2005 (2005)
We give regularity results for solutions of a parabolic equation in non-rectangular domains $U=\cup_{t\in ] 0,1[}\{ t\} \times I_{t}$ with $I_{t}=\{x:0$. The optimal regularity is obtained in the framework of the space $L^{p}$ with $p$ by considering the following cases: (1) When $\varphi (t)=t^{\alpha }, \alpha$ with a regular right-hand side belonging to a subspace of $L^{p}(U)$ and under assumption $\varphi (t)=t^{1/2}$ with a right-hand side taken only in $L^{p}(U)$. Our approach make use of the celebrated Dore-Venni results [2].
Classification : 35K05, 35K65, 35K90
Keywords: sum of linear operators, diffusion equation, non rectangular domain 
@article{EJDE_2005__2005__a148,
     author = {Labbas,  Rabah and Medeghri,  Ahmed and Sadallah,  Boubaker-Khaled},
     title = {An {\(L^p\)-approach} for the study of degenerate parabolic equations},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1073.35099},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a148/}
}
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Labbas,  Rabah; Medeghri,  Ahmed; Sadallah,  Boubaker-Khaled. An \(L^p\)-approach for the study of degenerate parabolic equations. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a148/