Partial regularity of minimizers of higher order integrals with (p,q)-growth

A simple partial regularity proof for minimizers of variational integrals

We consider multi-dimensional variational integrals F [u] := Ω f (·, u, Du) dx where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial C 1,α-regularity of minimizers of F. Our approach is based on the method of A-harmonic approximation, avoids the use of Gehring's lemma, and establishes partial regularity with the optimal Hölder expo...

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

Regularity of Minimizers of Integrals of the Calculus of Variations with Non Standard Growth Conditions

EXISTENCE AND REGULARITY OF MINIMIZERS OF NONCONVEX INTEGRALS WITH p− q GROWTH

We show that local minimizers of functionals of the form Z Ω [f(Du(x)) + g(x , u(x))] dx, u ∈ u0 + W 1,p 0 (Ω), are locally Lipschitz continuous provided f is a convex function with p − q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.