# Nonlinear Hodge equations in vector bundles

@article{Otway1998NonlinearHE, title={Nonlinear Hodge equations in vector bundles}, author={Thomas H. Otway}, journal={arXiv: Mathematical Physics}, year={1998} }

A gauge-invariant form of the nonlinear Hodge equations is studied. 1991 MSC: 58E15 (Classical field theory)

## 4 Citations

An elliptic inequality for nonlinear Hodge fields

- Mathematics
- 1998

A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.

Uniformly and nonuniformly elliptic variational equations with gauge invariance

- Mathematics
- 2000

A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak…

Nonlinear Hodge maps

- Mathematics
- 2000

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal,…

## References

SHOWING 1-10 OF 30 REFERENCES

An elliptic inequality for nonlinear Hodge fields

- Mathematics
- 1998

A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105

- Mathematics
- 1984

The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), will be forthcoming.

Connections withLP bounds on curvature

- Mathematics
- 1982

We show by means of the implicit function theorem that Coulomb gauges exist for fields over a ball inRn when the integralLn/2 field norm is sufficiently small. We then are able to prove a weak…

Classification of singular Sobolev connections by their holonomy

- Mathematics
- 1992

For a connection on a principalSU(2) bundle over a base space with a codimension two singular set, a limit holonomy condition is stated. In dimension four, finite action implies that the condition is…

Removable singularities in Yang-Mills fields

- Mathematics
- 1979

We show that a field satisfying the Yang-Mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite. We obtain the result that every…

Multiple Integrals in the Calculus of Variations

- Mathematics
- 1966

Semi-classical results.- The spaces Hmp and Hmp0.- Existence theorems.- Differentiability of weak solutions.- Regularity theorems for the solutions of general elliptic systems and boundary value…

N‐dimensional instantons and monopoles

- Mathematics
- 1980

The possibility of finding solutions of the instanton and monopole types to gauge field theories on arbitrary even and odd dimensional Euclidean manifolds respectively is investigated. Suitable…

Regularity for a class of non-linear elliptic systems

- Mathematics
- 1977

where ~ is a smooth positive function satisfying the ellipticity condition o(Q) + 2~'(Q)q > 0, V denotes the gradient, and [Vs[2 = ~ = 1 ]Vskl 2. This type of system arises as the EulerLagrange…