2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71721As a significant strengthening of properties of earlier algebras of generalized functions, here are presented classes of such algebras which can deal with dense singularities. In fact, the cardinal of the set of singular points can be larger than that of the nonsingular points. This large class of singularities allows the solution of large classes of smooth nonlinear PDEs. This in certain ways overcomes the celebrated 1957 H. Lewy impossibility result.Analysis of PDEsGeneral Relativity and Quantum CosmologyMathematical Physics35A,B,D,R, 46F30text