Symmetry and new solutions of the Black-Scholes equation.
Symmetry extensions and their physical reasons in the kinetic and hydrodynamic plasma models.
Symmetry group of Ţiţeica surfaces PDE.
Symmetry groups and conservation laws of certain partial differential equations.
Symmetry groups and Lagrangians associated with Tzitzeica surfaces.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry of minimizers with a level surface parallel to the boundary
We consider the functional where is a bounded domain and is a convex function. Under general assumptions on , Crasta [Cr1] has shown that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball. With some restrictions on , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these...
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
Systèmes mathématiques aux structures entremelées. Problèmes aux limites pour certains systèmes différentiels aux différences, ordinaires ou aux dérivées totales au sens de M. M. Picone
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.
Systems of meromorphic microdifferential equations
We introduce the notion of system of meromorphic microdifferential equations. We use it to prove a desingularization theorem for systems of microdifferential equations.
Systems of multi-dimensional Laplace transforms and a heat equation.
Syzygies of modules and applications to propagation of regularity phenomena.
Propagation of regularity is considered for solutions of rectangular systems of infinite order partial differential equations (resp. convolution equations) in spaces of hyperfunctions (resp. C∞ functions and distributions). Known resulys of this kind are recovered as particular cases, when finite order partial differential equations are considered.