Symmetry and concentration behavior of ground state in axially symmetric domains.
Symmetry and new solutions of the Black-Scholes equation.
Symmetry extensions and their physical reasons in the kinetic and hydrodynamic plasma models.
Symmetry groups and conservation laws of certain partial differential equations.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry of solutions of semilinear elliptic problems
We study symmetry properties of least energy positive or nodal solutions of semilinear elliptic problems with Dirichlet or Neumann boundary conditions. The proof is based on symmetrizations in the spirit of Bartsch, Weth and Willem (J. Anal. Math., 2005) together with a strong maximum principle for quasi-continuous functions of Ancona and an intermediate value property for such functions.
Symmetry of the barochronous motions of a gas.
Symmetry operators for the Fokker-Planck-Kolmogorov equation with nonlocal quadratic nonlinearity.
Symmetry operators of a Hartree-type equation with quadratic potential.
Symmetry properties for the extremals of the Sobolev trace embedding
Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations
We study uniformly elliptic fully nonlinear equations , and prove results of Gidas–Ni–Nirenberg type for positive viscosity solutions of such equations. We show that symmetries of the equation and the domain are reflected by the solution, both in bounded and unbounded domains.
Systèmes hyperboliques à multiplicité constante
Systems of Clairaut type
A characterization of systems of first order differential equations with (classical) complete solutions is given. Systems with (classical) complete solutions that consist of hyperplanes are also characterized.