On the quasi-linear elliptic PDE \({-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_k a_k \delta_{s_k}}\) in physics and geometry

DOI10.1007/s00220-012-1502-3zbMath1253.35058arXiv1107.4126OpenAlexW3125269714WikidataQ114230974 ScholiaQ114230974MaRDI QIDQ453345

Michael Karl-Heinz Kiessling

Publication date: 19 September 2012

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.4126

zbMATH Keywords

Minkowski spacetimeelectrostatic fieldMaxwell-Born-Infeld field equationsquasi-linear elliptic partial differential equation of divergence form

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Quasilinear elliptic equations (35J62)

Related Items (15)

On the electrostatic Born-Infeld equation with extended charges ⋮ Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences ⋮ Equilibrium measures and equilibrium potentials in the Born-Infeld model ⋮ On the Born-Infeld equation for electrostatic fields with a superposition of point charges ⋮ A sharp gradient estimate and \(W^{2, q}\) regularity for the prescribed mean curvature equation in the Lorentz-Minkowski space ⋮ Born-Infeld problem with general nonlinearity ⋮ On the regularity of the minimizer of the electrostatic Born-Infeld energy ⋮ Spacelike graphs with prescribed mean curvature on exterior domains in the Minkowski spacetime ⋮ Correction to: ``On the quasi-linear elliptic PDE \(-\nabla\cdot({\nabla}{u}/ \sqrt{1-|{\nabla}{u}|^2}) = 4\pi\sum_k a_k \delta_{s_k}\) in physics and geometry ⋮ Heteroclinic solutions of singular quasilinear bistable equations ⋮ The spectrum of the mean curvature operator ⋮ Extremals in nonlinear potential theory ⋮ On the Schrödinger spectrum of a hydrogen atom with electrostatic Bopp–Landé–Thomas–Podolsky interaction between electron and proton ⋮ Constructing graphs over \(\mathbb R^n\) with small prescribed mean-curvature ⋮ Some results on surfaces with different mean curvatures in \({\mathbb{R}}^{N+1}\) and \({\mathbb{L}}^{N+1} \)

Cites Work

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• Constructing graphs over \(\mathbb R^n\) with small prescribed mean-curvature
• Born-Infeld electrostatics in the complex plane
• Maximal surfaces in the 3-dimensional Minkowski space \(L^ 3\)
• Existence of maximal surfaces in asymptotically flat spacetimes
• Spacelike hypersurfaces with prescribed boundary values and mean curvature
• Area maximizing hypersurfaces in Minkowski space having an isolated singularity
• Regularity of variational maximal surfaces
• Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Solvability of the Dirichlet problem for the maximal surface equation with singularities in unbounded domains
• Born-Infeld particles and Dirichlet \(p\)-branes
• Electromagnetic field theory without divergence problems. I: The Born legacy
• Electromagnetic field theory without divergence problems. II: A least invasively quantized theory
• ON THE STATIC SPACETIME OF A SINGLE POINT CHARGE
• ON THE SPHERICALLY SYMMETRIC FIELD IN RELATIVITY
• Description of the set of singular entire solutions of the maximal surface equation
• N-Black hole stationary and axially symmetric solutions of the einstein/maxwell equations
• On the quantum theory of the electromagnetic field
• Foundations of the New Field Theory
• Classical solutions in the Born—Infeld theory
• Convergent perturbative power series solution of the stationary Maxwell–Born–Infeld field equations with regular sources
• SOME PROPERTIES OF THE SPECTRUM OF NONLINEAR EQUATIONS OF STURM-LIOUVILLE TYPE

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