Théorie du potentiel pour des opérateurs elliptiques non linéaires du second ordre à coefficients discontinus

Let Ω a open subset of ℝ n , n⩾3, and Ω⊂ $$\overline \omega$$ ⊂Ω an open. Existence and unicity are proved for the Dirichlet problem $$\left\{ \begin{gathered} \mathcal{L}u: = - \sum\nolimits_j {\frac{\partial }{{\partial x_j }}} \left( {\sum\nolimits_j {\alpha _{ij} \frac{{\partial u}}{{\partial x_i }} + \delta _j u} } \right) + \mathcal{B}( \cdot ,u,\nabla u) = 0, {\text{in }}\omega ; \hfill \\ u = g, {\text{on }}\partial \omega {\text{.}} \hfill \\ \end{gathered} \right.$$ It is assumed that the linear part of ℒ satisfy the conditions of Hervé, ℬ(·,u,∇u): Ω×ℝ×ℝ n →ℝ satisfy Carathéodory's condition and structure conditions (H1), (H2) and (H3) below. Let H denote the sheaf of L-solutions, we prove that (Ω,H) is a nonlinear Bauer harmonic space.