Nonlinear Problems Inspired by the Born--Infeld Theory of Electrodynamics

Abstract

It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude magnetic monopoles, achieving finite electromagnetic energy to relegate curvature singularities of charged black holes, and providing theoretical interpretation of equations of state of cosmic fluids via k-essence cosmology. Also discussed are some nonlinear differential equation problems.

arXiv comment30 pages. An invited survey article to appear in Advances in Nonlinear Studies

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Cited by in corpus (2)

• Compactness via monotonicity in nonsmooth critical point theory, with application to Born-Infeld type equations
• The Maxwell--Born--Infeld Theory: Presence of Finite-Energy Electric Point Charge and Absence of Monopole and Dyon