### On generalized Sobolev algebras and their applications

DOI: http://dx.doi.org/10.12775/TMNA.2005.019

#### Abstract

In the last two decades, many algebras of generalized functions

have been constructed, particularly the so-called generalized

Sobolev algebras. Our goal is to study the latter and some of

their main properties. In this framework, we pose and solve a

nonlinear degenerated Dirichlet problem with irregular data such

as Dirac generalized functions.

have been constructed, particularly the so-called generalized

Sobolev algebras. Our goal is to study the latter and some of

their main properties. In this framework, we pose and solve a

nonlinear degenerated Dirichlet problem with irregular data such

as Dirac generalized functions.

#### Keywords

Nonlinear degenerate Dirichlet problem; generalized solution; Sobolev algebra; non positive solution

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