Local regularity results for minima of anisotropic functionals and solutions of anisotropic equations.

Hongya, Gao; Jinjing, Qiao; Yong, Wang; Yuming, Chu

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Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order $q > 2$ are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension $n$ is less than or equal to $q + 2$ .

Regularity of minimizers for nonconvex vectorial integrals with $p - q$ growth via relaxation methods.

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Regularity results for a class of obstacle problems

Michela Eleuteri (2007)

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A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction

Yves Capdeboscq, Michael S. Vogelius (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.