Mythily Ramaswamy

An improved Hardy-Sobolev inequality and its application

For\Omega \subset

Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients

IR^n

Hybrid Control Systems and Viscosity Solutions

,n\geq 2, a bounded domain, and for 1 < p < n, we improve the Hardy-Sobolev inequality, by adding a term with a singular weight of the type \frac{1}{log(1/|x|)}

Existence of positive solutions of some semilinear elliptic equations with singular coefficients

^2

Controllability and Stabilizability of the Linearized Compressible Navier--Stokes System in One Dimension

. We show that this weight function is optimal in the sense that the inequality fails for any other weight function more singular than this one. Moreover, we show that a series of finite terms can be added to improve the Hardy-Sobolev inequality, which answers a question of Brezis-Vazquez. Finally, we use this result to analyze the behaviour of the first eigenvalue of the operator L\mu\omega := -(div(|\nabla\upsilon|{p-2}\nabla\upilson)as \mu increases to \frac{n-p}{p}

Symmetry of positive solutions of some nonlinear equations

^p

Self-similar solutions of a generalized Burgers equation with nonlinear damping

for 1 < p < n.

Chapter 4 - Symmetry of Solutions of Elliptic Equations via Maximum Principles

We establish uniqueness or comparison results for a class of Hamilton-Jacobi equations and give characterizations of maximal solutions of Hamilton-Jacobi equations. The results are applied to characterizing value functions of exit time problems in optimal control. 12 refs.

GLOBAL BIFURCATION FOR SEMILINEAR ELLIPTIC PROBLEMS

We investigate a model of hybrid control system in which both discrete and continuous controls are involved. In this general model, discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where the controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. We prove the continuity of the associated value function V with respect to the initial point. Using the dynamic programming principle satisfied by V, we derive a quasi-variational inequality satisfied by V in the viscosity sense. We characterize the value function V as the unique viscosity solution of the quasi-variational inequality by the comparison principle method.

Some elliptic semilinear indefinite problems on R

In this paper, we consider the semilinear elliptic problem in a bounded domain \Omega \subseteq