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Currently displaying 1 – 4 of 4

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A new partial regularity proof for solutions of nonlinear elliptic systems.

Christoph Hamburger — 1998

Manuscripta mathematica

Partial regularity for minimizers of variational integrals with discontinuous integrands

Christoph Hamburger — 1996

Annales de l'I.H.P. Analyse non linéaire

Partial Boundary Regularity of Solutions of Nonlinear Superelliptic Systems

Christoph Hamburger — 2007

Bollettino dell'Unione Matematica Italiana

We prove global partial regularity of weaksolutions of the Dirichlet problem for the nonlinear superelliptic system $\operatorname{div}A(x,u,Du)+B(x,u,DU)=0$ , under natural polynomial growth of the coefficient functions $A$ and $B$ . We employ the indirect method of the bilinear form and do not use a Caccioppoli or a reverse Hölder inequality.

Optimal partial regularity of minimizers of quasiconvex variational integrals

Christoph Hamburger — 2007

ESAIM: Control, Optimisation and Calculus of Variations

We prove partial regularity with optimal Hölder exponent of vector-valued minimizers of the quasiconvex variational integral $\int F (x, u, D u) d x$ under polynomial growth. We employ the indirect method of the bilinear form.

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