Faculté des sciences

Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data

Augsburger, Fabien ; Hungerbühler, Norbert

In: Electronic Journal of Differential Equations, 2004, vol. 144, p. 1-18

We study the quasilinear elliptic system −div σ(x, u,Du) = v(x) + f(x, u) + div g(x, u) on a bounded domain of Rⁿ with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source v in a moving and dissolving substance, where the motion is described by g and the dissolution by f. We prove existence of a weak solution of this system under classical... Plus

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    Summary
    We study the quasilinear elliptic system −div σ(x, u,Du) = v(x) + f(x, u) + div g(x, u) on a bounded domain of Rⁿ with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source v in a moving and dissolving substance, where the motion is described by g and the dissolution by f. We prove existence of a weak solution of this system under classical regularity, growth, and coercivity conditions for σ, but with only very mild monotonicity assumptions.