How to solve smooth nonlinear pdes in algebras of generalized functionswith dense singularities

Abstract

As 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 singularpoints can be large than that o the nonsingular points. This large class ofsingularities allows the solution of large classes of smooth nonlinear PDEs. This in certain way overcomes the celebrated 1957 H. Lewy impossibility result.

Keywords:

• Dense singularities
• Smooth nonlinear PDEs
• Generalized solutions
• Type independence existence results
• The H. Lewy impossibilit

AMS:

• 46F30
• 35A
• B
• D
• R