Elliptic Problems with Superlinear Convection Terms
Copyright policy )Elliptic Problems with Superlinear Convection Terms
In this manuscript we deal with elliptic equations with superlinear first order terms in divergence form of the following type \[ -\mbox{div}(M(x)\nabla u)= -\mbox{div}(h(u)E(x))+f(x), \] where $M$ is a bounded elliptic matrix, the vector field $E$ and the function $f$ belong to suitable Lebesgue spaces, and the function $s\to h(s)$ features a superlinear growth at infinity. We provide some existence and non existence results for solutions to the associated Dirichlet problem and a comparison principle.
- University of Vienna Austria
- University of Catania Italy
- Sapienza University of Rome Italy
- University Federico II of Naples Italy
Non coercive operators, Semilinear elliptic equations, existence, Non coercive operators; Superlinear convection terms, uniqueness, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, FOS: Mathematics, Superlinear convection terms, semilinear elliptic equation, Dirichlet problem, Analysis of PDEs (math.AP)
Non coercive operators, Semilinear elliptic equations, existence, Non coercive operators; Superlinear convection terms, uniqueness, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, FOS: Mathematics, Superlinear convection terms, semilinear elliptic equation, Dirichlet problem, Analysis of PDEs (math.AP)
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