XXVII Workshop on Geometric Methods in Physics 29.06-05.07.2008

Serguei Samborski

Functional Spaces, Differential Calculus and Nonclassical Solutions of Nonlinear PDE

Two problems (a generalisation of Differential Calculus and Extensions of Partial Differential Operators provided nonclassical solutions, in particular Viscosity solutions) illustrate that there are convinient solutions of Problems in the class of topological functional spaces with closed algebraic operations. These Problems can't be solved in Spaces with usual condition of the continuity of the algebraic operations.