Regularity of absolute minimizers for continuous convex Hamiltonians

Partial Regularity for Almost Minimizers of Quasi-Convex Integrals

We consider almost minimizers of variational integrals whose integrands are quasiconvex. Under suitable growth conditions on the integrand and on the function determining the almost minimality, we establish almost everywhere regularity for almost minimizers and obtain results on the regularity of the gradient away from the singular set. We give examples of problems from the calculus of variatio...

Partial regularity for quasi minimizers

Lipschitz regularity for constrained local minimizers of convex variational integrals with a wide range of anisotropy

We establish interior gradient bounds for functions u ∈ W 1 1,loc (Ω) which locally minimize the variational integral J[u, Ω] = ∫ Ω h (|∇u|) dx under the side condition u ≥ Ψ a.e. on Ω with obstacle Ψ being locally Lipschitz. Here h denotes a rather general N-function allowing (p, q)-ellipticity with arbitrary exponents 1 < p ≤ q < ∞. Our arguments are based on ideas developed in [BFM] combined...

Partial Regularity for Minimizers of Quasi-convex Functionals with General Growth

holds for every A ∈ R and every smooth ξ : B1 → R with compact support in the open unit ball B1 in R . By Jensen’s inequality, quasi convexity is a generalization of convexity. It was originally introduced as a notion for proving the lower semicontinuity and the existence of minimizers of variational integrals. In fact, assuming a power growth condition, quasi convexity is proved to be a necess...

Regularity of split-type Hamiltonians for quilts

Suppose M = M0 × . . . × MN is a product symplectic manifold. We show that, under certain hypotheses, there is a Hamiltonian perturbation of split-type for which all perturbed pseudoholomorphic curves are regular.