Quasilinear Elliptic Systems in Divergence Form with Weak Monotonicity
نویسنده
چکیده
We consider the Dirichlet problem for the quasilinear elliptic system − div σ(x, u(x), Du(x)) = f on Ω u(x) = 0 on ∂Ω for a function u : Ω → Rm, where Ω is a bounded open domain in Rn. For arbitrary right hand side f ∈W−1,p (Ω) we prove existence of a weak solution under classical regularity, growth and coercivity conditions, but with only very mild monotonicity assumptions.
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