Regularity under Sharp Anisotropic General Growth Conditions

Partial Regularity under Anisotropic (p,q) Growth Conditions

Partial Regularity For Higher Order Variational Problems Under Anisotropic Growth Conditions

We prove a partial regularity result for local minimizers u : Rn ⊃ Ω → RM of the variational integral J(u,Ω) = ∫ Ω f(∇ku) dx, where k is any integer and f is a strictly convex integrand of anisotropic (p, q)–growth with exponents satisfying the condition q < p(1 + 2 n). This is some extension of the regularity theorem obtained in [BF2] for the case n = 2.

Nonlinear Anisotropic Elliptic and Parabolic Equations in R with Advection and Lower Order Terms and Locally Integrable Data

We prove existence and regularity results for distributional solutions in RN for nonlinear elliptic and parabolic equations with general anisotropic diffusivities as well as advection and lower-order terms that satisfy appropriate growth conditions. The data are assumed to be merely locally integrable.

Sharp trace regularity for an anisotropic elasticity system

In this paper, we establish an optimal trace regularity theorem, also known as the hidden regularity theorem [L2], for the anisotropic linear elasticity equation on a bounded domain Ω with Lipschitz boundary. In its simplest form it provides a space-time L estimate for the trace of the normal derivative for the solution. Over the years, such sharp trace regularity theorems have proven to be cru...

Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes SUSHI: a scheme using stabilisation and hybrid interfaces

A discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces which may for instance be chosen at the diffusion tensor discontinuities. The scheme is therefore completely cell centred if no edge unknown is kept. It is shown to be ...