Limiting behavior of solutions of a sequence of non-homogeneous boundary value problems (Q2712729)

Let \(\Omega\) be a domain in \(\mathbb{R}^n\). The author considers a sequence of nonhomogeneous boundary value problems NEWLINE\[NEWLINEL_m u_m= h_m\quad\text{in }\Omega,\quad \partial^\omega u_m|_{\partial\Omega}= \psi_{\omega m},\quad |\omega|\leq t_m-1.\tag{1\(_m\)}NEWLINE\]NEWLINE Here \(L_m\) \((m\geq 1)\) is a nonlinear differential operator of order \(t_m\leq\infty\), written in a divergence form, and \(u_m\) is in a Sobolev space of infinite order.NEWLINENEWLINENEWLINEPrincipal result: If the sequences of operators \(L_m\) and functions \(h_m\), \(\psi_{\omega m}\) converge in a certain sense to an operator \(L_\infty\) and functions \(h_\infty\), \(\psi_{\omega\infty}\), then a sequence \((u_m)_m\) of solutions to the problems \((1_m)\) has an accumulation point, which is a solution to the limiting problem \((1_\infty)\). No proofs.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00028].