Some critical point theorems and applications to semilinear elliptic partial differential equations
Some decay properties for the damped wave equation on the torus
This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...
Some estimates of Schrödinger-type operators with certain nonnegative potentials.
Some estimates of solutions to Monge-Ampère type equations in dimension two
Some exact estimates of weak solutions to a mixed boundary value problem for nonlinear equations in domains with nonsmooth boundary.
Some exact Solutions of the Korteweg-de Vries Equation with Variable Coefficients
Some geometric aspects of the calculus of variations in several independent variables
This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.
Some Linear Elliptic Selfsimilar Equations with Whirl-Like Solutions.
Some notes to certain modification of the Oseen problem
Some notes to the transport equation and to the Green formula
Some properties of stationary parabolic mixed problems in an infinite cylinder
Some relatively new techniques for nonlinear problems.
Some remarks on gradient estimates for heat kernels.
Some remarks on Prandtl system
The purpose of this paper is to correct some drawbacks in the proof of the well-known Boundary Layer Theory in Oleinik’s book. The Prandtl system for a nonstationary layer arising in an axially symmetric incopressible flow past a solid body is analyzed.
Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations
This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.
Some remarks on the continuity equation
This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.
Some solutions for a class of singular equations
In this paper we obtain all solutions which depend only on for a class of partial differential equations of higher order with singular coefficients.
Some weighted Hardy-type inequalities on anisotropic Heisenberg groups.
Sophus Lie a harmonie v matematické fyzice (k 150. výročí narození)
Source type positive solutions of nonlinear parabolic inequalities