## Quasilinear elliptic systems in divergence form with weak monotonicity.(English)Zbl 0920.35060

Summary: We consider the Dirichlet problem for the quasilinear elliptic system $-\text{div }\sigma(x, u(x), Du(x))= f\quad\text{in }\Omega,\quad u(x)= 0\quad\text{on }\partial\Omega$ for a function $$u: \Omega\to \mathbb{R}^m$$, where $$\Omega$$ is a bounded open domain in $$\mathbb{R}^n$$. For arbitrary right-hand side $$f\in W^{-1,p'}(\Omega)$$ we prove existence of a weak solution under classical regularity, growth and coercivity conditions, but with only very mild monotonicity assumptions.

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations 47J05 Equations involving nonlinear operators (general) 35J55 Systems of elliptic equations, boundary value problems (MSC2000)

Young measures
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