Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equationsSolutions visqueuses du problème avec une dérivée oblique dégénérée pour une classe d'équations complètement non linéaires

In this paper we prove a comparison principle between the semicontinuous viscosity sub- and supersolutions of the tangential oblique derivative problem and the mixed Dirichlet–Neumann problem for fully nonlinear elliptic equations. By means of the comparison principle, the existence of a unique viscosity solution is obtained. To cite this article: P. Popivanov, N. Kutev, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 661–666.     

Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations

A new ordinary differential inequality without global solutions is proposed. Comparison with similar differential inequalities in the well‐known concavity method is performed. As an application, finite time blow up of the solutions to nonlinear Klein–Gordon equation and generalized Boussinesq equation is proven. The initial energy is arbitrary high positive. The structural conditions on the initial data generalize the assumptions used in the literature for the time being. Copyright © 2015 John Wiley & Sons, Ltd.     

A second-order boundary value problem with impulsive effects on an unbounded domain

We study a second-order nonlinear differential equation on an unbounded domain with solutions subject to impulsive conditions and the Sturm–Liouville type boundary conditions. The existence results are obtained via applications of Krasnosel’ski?’s fixed point theorem for the sum of a completely continuous operator and a contraction.     

Sharp Hardy Inequalities in Star-shaped Domains with Double Singular Kernels

Improved Hardy inequality with double singular kernel in bounded, star-shaped domains \(\Omega \subset R^n\) is proved. The case of singularity at an interior point and on the boundary of the domain is considered. The Hardy constant is optimal and the inequality is sharp due to the additional term.     

Nontrivial solutions for Monge-Ampère type operators in convex domains

In this paper we prove existence and interior regularity of convex solutions of the Dirichlet problem for a class of Monge-Ampère type equations with right hand side vanishing on the boundary, by means of the fixed point index theory for Bakelman's weak solutions. The regularity in the interior follows from recent results of Caffarelli. Partially supported by M.U.R.S.T., Italy Partially supported by G.N.A.F.A. of C.N.R., Italy. This work was accomplished during a Humbold research stay at Karlsruhe and Heidelberg Universities.     

On free p-superalgebras

In this article we consider several aspects of algebraic combinatorics and combinatorial algebra over fields of prime characteristics. P-super-Radford theorem gives the structure of the free associative algebra over a field of prime characteristic with the new multiplication given by the super shuffle product, we show that this algebra is isomorphic to the reduced free super commutative algebra on s-regular words. We prove the elimination theorem for free partially commutative color Lie p-superalgebras and obtain a Schreier type formula for free Lie p-superalgebras using formal power series techniques.     

Interior Boundaries for Degenerate Elliptic Equations and Viscosity Solutions

Linear elliptic equations which are degenerate elliptic on a closed interior surface Γ which divides in two separate parts the original domain are considered. Existence and uniqueness of a viscosity solution in the whole domain and in every of the subdomains is proved under some conditions on the geometry of Γ.     

Formation of charged defects during the nitridation of a metal particle

A model explaining and predicting generation of a temporal electric potential during nitridation of a single metal pellet has been developed. The model takes into account the kinetics of defects formation and assumes that the rate of the chemical reaction can be described by the shrinking-core process. The model simulations have shown that time scale of the generated electric potential depends on both the initial nitride shell thickness and heat removal from the particle surface. At thin initial shell and low rate of heat removal the maximum of the surface electric potential is attained before the temperature and surface nitrogen concentration have reached their maximums but after the maximum of nitridation has appeared. Quasi-neutral distributions of metal vacancies and electron holes are formed at the maximum temperature. At thick initial shell and/or high rates of heat removal from the particle surface the potential maximum may be observed much later: after the maximum temperature has been achieved. Correspondingly, non-equilibrium concentrations of the charged defects exist till the end of nitridation. In contrast to oxidation the nitrogen adsorption rate constants (the activation energy and pre-exponent) have negligible effect on the surface potential form and amplitude. At the ignition limit the rate of nitridation is proportional to the power of −1/2 for the ambient nitrogen pressure in the proposed scheme of defects formation. Metal vacancies and electron holes are the main charged defects in nitrides during nitrogen combustion. The nitride formation is limited by transfer of the vacancies in nitride.