Abstract:In this note, we establish sharp regularity for solutions to the following generalized p-Poisson equation − div A∇u, ∇u p−2 2 A∇u = − div h + f in the plane (i.e. in R 2 ) for p > 2 in the presence of Dirichlet as well as Neumann boundary conditions and with h ∈ C 1−2/q , f ∈ L q , 2 < q ≤ ∞. The regularity assumptions on the principal part A as well as that on the Dirichlet/Neumann conditions are exactly the same as in the linear case and therefore sharp (see Remark 2.8 below). Our main results Theorem 2.6 an… Show more
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