Adding Caccioppoli-type estimates in Machine Learning part1
<p>We obtain Caccioppoli — type estimates for nontrivial and nonnegative solutions to the anticoercive partial differential inequalities of elliptic type involving degenerated p — Laplacian: $-Δ_{p,a} u:= -\mathrm{div}(a(x)|\na u|^{p-2}\na u)\ge b(x)Φ(u)$, where u is defined in a domain Ω. Using Caccioppoli — type estimates, we obtain several variants of Hardy — type inequalities in weighted Sobolev spaces.</p>
<p>2.Caccioppoli-type estimates and H-Matrix approximations to inverses for FEM-BEM couplings (arXiv)</p>
<p>Author : Markus Faustmann, Jens Markus Melenk, Maryam Parvizi</p>
<p>Abstract : We consider three different methods for the coupling of the finite element method and the boundary element method, the Bielak-MacCamy coupling, the symmetric coupling, and the Johnson-Nédélec coupling. For each coupling we provide discrete interior regularity estimates. As a consequence, we are able to prove the existence of exponentially convergent H-matrix approximants to the inverse matrices corresponding to the lowest order Galerkin discretizations of the couplings</p>
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