A necessary and sufficient condition for the diagonalization of multi-dimensional quasilinear systems.
A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems
This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained...
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the hamiltonian. The proof relies on a reverse Hölder inequality.
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse Hölder inequality.
A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations
In Albano-Cannarsa [1] the authors proved that, under some conditions, the singularities of the semiconcave viscosity solutions of the Hamilton-Jacobi equation propagate along generalized characteristics. In this note we will provide a simple proof of this interesting result.
Adjoint methods for obstacle problems and weakly coupled systems of PDE
The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.
Almost continuous solutions of geometric Hamilton–Jacobi equations
Analyticité locale pour les solutions de l'équation d'Euler