Failure of Fredholm solvability for the Dirichlet problem corresponding to weakly elliptic systems (Q2030276)

This paper is devoted to the study of the higher-dimensional version of systems which are weakly elliptic for which the \(L^p\)-Dirichlet problem in the upper half-space \(\mathbb{R}_+^n\), \(n\geq 2\), with traces considered in the nontangential sense is not Fredholm solvable. In fact, the authors prove that such a problem has an infinite dimensional space of null-solutions and its space of admissible boundary data has infinite codimension in \([L^p(\mathbb{R}^{n-1})]^n\).