Regularity results for local minimizers of energies with general densities having superquadratic growth

We consider variational integrals whose energy densities are represented by N-functions h of at least quadratic growth. Under rather general conditions on h almost everywhere regularity of vector-valued local minimizers is established, and it is possible to include the case of higher order variational problems without essential changes in the arguments

Local Lipschitz regularity of vector valued local minimizers of variational integrals with densities depending on the modulus of the gradient

If u:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{M} locally minimizes the functional \int_{\Omega}h(\left|\nabla u\right|)dx with h such that \frac{h\u27(t)}{t}\leq h\u27\u27(t)\leq c(t+t^{2})^{\omega}\frac{h\u27(t)}{t} for all t\geq0, then u is locally Lipschitz independent of the value of \omega\geq0

A remark on the global Lipschitz regularity of solutions to inner obstacle problems involving degenerate functionals of p-growth

We extend some recent results of Jagodziński, Olek and Szczepaniak [JOS] on the Lipschitz character of solutions to inner obstacle problems associated to a uniformly elliptic operator to the case of nonlinear, degenerate operators

Static Properties of a Simulated Supercooled Polymer Melt: Structure Factors, Monomer Distributions Relative to the Center of Mass, and Triple Correlation Functions

We analyze structural and conformational properties in a simulated bead-spring model of a non-entangled, supercooled polymer melt. We explore the statics of the model via various structure factors, involving not only the monomers, but also the center of mass (CM). We find that the conformation of the chains and the CM-CM structure factor, which is well described by a recently proposed approximation [Krakoviack et al., Europhys. Lett. 58, 53 (2002)], remain essentially unchanged on cooling toward the critical glass transition temperature of mode-coupling theory. Spatial correlations between monomers on different chains, however, depend on temperature, albeit smoothly. This implies that the glassy behavior of our model cannot result from static intra-chain or CM-CM correlations. It must be related to inter-chain correlations at the monomer level. Additionally, we study the dependence of inter-chain correlation functions on the position of the monomer along the chain backbone. We find that this site-dependence can be well accounted for by a theory based on the polymer reference interaction site model (PRISM). We also analyze triple correlations by means of the three-monomer structure factors for the melt and for the chains. These structure factors are compared with the convolution approximation that factorizes them into a product of two-monomer structure factors. For the chains this factorization works very well, indicating that chain connectivity does not introduce special triple correlations in our model. For the melt deviations are more pronounced, particularly at wave vectors close to the maximum of the static structure factor.Comment: REVTeX4, 16 pages, 16 figures, accepted for publication in Physical Review