We investigate the homogeneous Dirichlet problem for a class of second-order elliptic partial differential equations with a quadratic gradient term and singular data, arising for instance in the theory of non-Newtonian fluids of type Callegari-Nachman and also of heat conduction in electrically conducting materials of type Cohen-Keller. In particular, we study the asymptotic behavior of the solution near the boundary under suitable assumptions on the growth of the coefficients of the equation.
Problems for elliptic singular equations with a quadratic gradient term
VITOLO, Antonio
2007
Abstract
We investigate the homogeneous Dirichlet problem for a class of second-order elliptic partial differential equations with a quadratic gradient term and singular data, arising for instance in the theory of non-Newtonian fluids of type Callegari-Nachman and also of heat conduction in electrically conducting materials of type Cohen-Keller. In particular, we study the asymptotic behavior of the solution near the boundary under suitable assumptions on the growth of the coefficients of the equation.File in questo prodotto:
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