Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems

In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(a(x, Du)+ F(u)) ■ f in Ω, where f ∈ L1 Ω. A vector field a(·,·) is a Carath′eodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.     

Entropy solutions of anisotropic elliptic nonlinear obstacle problem with measure data

We prove the existence of an entropy solution for a class of nonlinear anisotropic elliptic unilateral problem associated to the following equation $$\begin{aligned} -\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) -\sum _{i=1}^{N}\partial _{i}\phi _{i}( u)=\mu , \end{aligned}$$where the right hand side $$\mu $$ belongs to $$L^{1}(\Omega )+ W^{-1, \vec {p'}}(\Omega )$$. The operator $$-\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) $$ is a Leray–Lions anisotropic operator and $$\phi _{i} \in C^{0}({\mathbb {R}}, {\mathbb {R}})$$.     

Variational Inequalities for Combined Control and Stopping Game

Abstract

We study a nonlinear elliptic variational inequality associated with the combined stochastic control problem. By using the dynamic programming principle and the method of penalization, we establish the existence of a unique viscosity solution of the variational inequality and describe it as the value function of the corresponding combined stochastic game problem.     

Infinite Horizon Reflected Backward SDEs with Jumps and RCLL Obstacle

Abstract

In this article, we deal with the one-dimensional reflected backward stochastic differential equation with one or two barriers for infinite horizon when the noise is driven by a Brownian motion and an independent Poisson point process. The reflecting process is right continuous with left limits whose jumps are whatever. The authors prove existence and uniqueness of the solution by using a method based on a combination of penalization and the Snell envelope theory. Once more we use a contraction to show the result in the general framework.     

Existence of a Renormalised Solutions for a Class of Nonlinear Degenerated Parabolic Problems with L1 Data

We study the existence of renormalized solutions for a class of nonlinear degenerated parabolic problem. The Carathéodory function satisfying the coercivity condition, the growth condition and only the large monotonicity. The data belongs to L^1(Ω).     

The replacement of a phenol group by an aniline or acetanilide group enhances the cytotoxicity of 2-ferrocenyl-1,1-diphenyl-but-l-ene compounds against breast cancer cells

We have previously shown that conjugated ferrocenyl p-phenols show strong cytotoxic effects against both the hormone-dependent MCF-7 and hormone-independent MDA-MB-231 breast cancer cell lines, possibly via oxidative quinone methide formation. We now present a series of analogous amine and acetamide compounds: 2-ferrocenyl-1-(4-aminophenyl)-1-phenyl-but-1-ene (Z+E-2), 2-ferrocenyl-1-(4-N-acetylaminophenyl)-1-phenyl-but-1-ene (Z-3), and their corresponding organic molecules 1-(4-aminophenyl)-1,2-bis-phenyl-but-1-ene (Z+E-4) and 1-(4-N-acetamidophenyl)-1,2-bis-phenyl-but-1-ene (Z+E-5). All of the compounds have adequate relative binding affinity values for the estrogen receptor; between 2.8% and 5.7% for ERα, and between 0.18% and 15.5% for ERβ, as well as exothermic ligand binding in in silico ER docking experiments. Compounds 2 and 3 show dual estrogenic/cytotoxic activity on the MCF-7 cell line; they are proliferative at low concentrations (0.1 μM) and antiproliferative at high concentrations (10 μM). On the MDA-MB-231 cell line, the ferrocenyl complexes 2 and 3 are antiproliferative with IC₅₀ values of 0.8 μM for 2 and 0.65 μM for 3, while the purely organic molecules 4 and 5 show no effect. Electrochemical experiments suggest that both 2 and 3 can be transformed to oxidized quinoid-type species, analogous to what had previously been observed for the ferrocene phenols.     

Application of the NRL tight-binding method to the heavy elements Pb and Po

We have applied the NRL tight-binding (TB) method to study the mechanical and electronic properties of the heavy elements Pb and Po. The predicted properties include ground-state structure, electronic band structure and elastic moduli. Phonon-dispersion curves at T=0 K were also determined. As demonstrated in this paper, the results are in good agreement with the full potential linearized augmented plane wave calculations and the available experimental data. In addition, we performed molecular-dynamics simulations to obtain various temperature-dependent quantities of Pb such as the atomic mean-square displacement, Debye-Waller factor and thermal expansion coefficient. With our TB we have also calculated the vacancy formation energy of Pb. Finally, we report on the effects of spin-orbit coupling, through our TB scheme, on electronic structure and energetic properties.     

L~∞-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms

In this work,we will prove the existence of bounded solutions in W_0~(1,p)(Ω)∩L~∞(Ω) for nonlinear elliptic equations-div(a(x,u,▽u))+g(x,u,▽u)+H(x,▽u) =f,where a,g and H are Caratheodory functions which satisfy some conditions,and the right hand side/belongs to W~(-1,q)(Ω).