Solvability Of Operator Equations And Periodic Solutions Of Semilinear Hyperbolic Equations
Solvability of the Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains.
Solvable two-body Dirac equation as a potential model of light mesons.
Solving the Degenerate Complex Monge-Ampère Equation with One Concentrated Singularity.
Some applications of parabolic comparison principles to the study of decay estimates.
Some boundary value problems for systems of linear partial differential equations of hyperbolic type.
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
We consider three types of semilinear second order PDEs on a cylindrical domain , where is a bounded domain in , . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of is reserved for time , the third type is an elliptic equation with a singled out unbounded variable . We discuss the asymptotic behavior, as , of solutions which are defined and bounded on .
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Some continuation properties via minimax arguments.
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 elementary inequalities in gas dynamics equation.
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 Examples For Nonlinear Superposition
Some examples for nonlinear superposition.
Some examples for the extended use of the parametric representation method
Some existence results for the scalar curvature problem via Morse theory
We prove existence of positive solutions for the equation on , arising in the prescribed scalar curvature problem. is the Laplace-Beltrami operator on , is the critical Sobolev exponent, and is a small parameter. The problem can be reduced to a finite dimensional study which is performed with Morse theory.
Some geometric properties for a class of non-Lipschitz domains.
Some Gradient Estimates on Covering Manifolds
Let M be a complete Riemannian manifold which is a Galois covering, that is, M is periodic under the action of a discrete group G of isometries. Assuming that G has polynomial volume growth, we provide a new proof of Gaussian upper bounds for the gradient of the heat kernel of the Laplace operator on M. Our method also yields a control on the gradient in case G does not have polynomial growth.