A formula is given for recovering the boundary values of the coeÆcient of an elliptic operator, div r, from the Dirichlet to Neumann map. The main point is that one may recover without any a priori smoothness assumptions. The formula allows one to recover the value of pointwise. Let R; n 2, be a bounded open set with Lipschitz boundary and let : ! R satisfy 1 (x) for some > 0. Let L = div r be...

We study H(div) preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for a weighted, stochastic H(div) operator, acting on a certain tensor product space of random fields with finite variance. We build on the Arnold-Falk-Winther multigrid algorithm pres...

As a model problem for the miscible and imiscible two phase ow we consider the following system of partial diierential equations: ?div (a(c; x) (rp(x; t) + (c; x))) = 0 @tc(x; t) + div (u(x; t)c(x; t)) ? div (rc(x;t)) = f(x; t); with (x; t) 2 (0; T). Here u denotes the Darcy velocity, p the pressure and c the concentration of one phase of the uid. For small diiusions (0 < < < 1) standard Galerk...

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u|p(x)−2∇u) + |u|p(x)−2u = λa(x)|u|γ(x)−2u+ Fu(x, u, v) in R , − div |∇v|q(x)−2∇v) + |v|q(x)−2v = λb(x)|v|δ(x)−2v + Fv(x, u, v) in R , u ∈W 1,p(·)(RN ), v ∈W 1,q(·)(RN ), where the corresponding functional does not satisfy PS conditions. We obtain a suffici...

We prove Calderón-Zygmund estimates for a class of parabolic problems whose model is the non-homogeneous parabolic p(x, t)-Laplacian equation ∂tu − div ( |Du|p(x,t)−2Du ) = f − div ( |F|p(x,t)−2F ) . More precisely, we will show that the spatial gradient Du is as integrable as the inhomogeneities f and F, i.e. |F|p(x,t), | f | γ1 γ1−1 ∈ L loc ⇒ |F| p(x,t) ∈ L loc for any q > 1, where γ1 is the ...

We consider the Cauchy-Dirichlet Problem for a nonlinear parabolic equation with L data. We show how the concept of kinetic formulation for conservation laws [LPT94] can be be used to give a new proof of the existence of renormalized solutions. To illustrate this approach, we also extend the method to the case where the equation involves an additional gradient term. We consider the question of ...

Functional eukaryotic voltage-gated Na+ (NaV) channels comprise four domains (DI-DIV), each containing six membrane-spanning segments (S1-S6). Voltage sensing is accomplished by the first four membrane-spanning segments (S1-S4), which together form a voltage-sensing domain (VSD). A critical NaV channel gating process, inactivation, has previously been linked to activation of the VSDs in DIII an...

Non-proliferating cells, such as mature neurons, are generally believed to be more resistant to X-rays than proliferating cells, such as glial and vascular endothelial cells. Therefore, the late adverse effects of radiotherapy on the brain have been attributed to the radiation-induced damage of glial and vascular endothelial cells. However, little is known about the radiosensitivities of neuron...

Let Sn = K[[x1, . . . , xn]] be the algebra of power series over a field K of characteristic zero, S c n be the group of continuous automorphisms of Sn with constant Jacobian, and Div c n be the Lie algebra of derivations of Sn with constant divergence. We prove that AutLie(Div c n) = AutLie,c(Div c n) ≃ S c n.

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