W^{1,1}_0 minima of non coercive functionals

TL;DR

This paper investigates a specific type of mathematical functional that is not coercive, demonstrating the existence of a minimum within a particular function space, which advances understanding of such functionals in analysis.

Contribution

It establishes the existence of minima for non coercive functionals in W^{1,1}_0, a result not previously confirmed for this class of problems.

Findings

Existence of a minimum in W^{1,1}_0 for non coercive functionals

Extension of variational methods to non coercive cases

New insights into the behavior of non coercive functionals

Abstract

We study an integral non coercive functional defined on H^1_0, proving the existence of a minimum in W^{1,1}_0.