Affiliation:
1. Dipartimento di Matematica Applicata Università degli Studi di Pisa Via F. Buonarroti 1/c, Pisa, ITALY and Department of Mathematics, College of Science King Saud University Riyadh, 11451, SAUDI ARABIA
Abstract
Abstract
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think of
with Dirichlet boundary conditions in a bounded open star-shaped set. Having this problem in mind, we construct a new class of functions called ultrafunctions in which the above problem has a (generalized) solution. In this construction, we apply the general ideas of Non Archimedean Mathematics (NAM) and some techniques of Non Standard Analysis. Also, some possible applications of ultrafunctions are discussed.
Subject
General Mathematics,Statistical and Nonlinear Physics
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