The Calderón projector for an elliptic operator in divergence form.
The Calderón projector was first introduced by Calderón in [Lecture Notes on pseudodifferential operators and boundary value problems, I. A. M. CONICET, Bs. As.], for elliptic operators with \(C^{\infty}\) coefficients in a \(C^{\infty}\) domain. For the Laplace operator, the results of \textit{E. B. Fabes}, \textit{M. Jodeit jun.} and \textit{N. M. Rivière}, Acta Math. 141, 165--186 (1978; Zbl 0402.31009)] show that, on \(C^1\) domains, the Calderón projector is bounded on \(L^p(\partial\Omega)\times L^p(\partial\Omega)\) for all \(1<p<+\infty\). In the present paper, similar results are obtained for second order elliptic operators in divergence form \(L=-\text{div }A\nabla\) on \(C^1\) domains when the entries of \(A\) are Lipschitz functions. The construction is done by means of the layer potentials.
scientific article; zbMATH DE number 1757477