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.
The Bernoulli manifolds for nonelliptic quasilinear systems of first order and applications in continuum mechanics
The differential form method for finding symmetries.
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The group structure of supergravity
The positive radial solutions of a class of semilinear elliptic equations.
The role of symmetry and separation in surface evolution and curve shortening.