We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.
We consider a free boundary value problem for a viscous, incompressible fluid contained in an uncovered three-dimensional rectangular channel, with gravity and surface tension, governed by the Navier-Stokes equations. We obtain existence results for the linear and nonlinear time-dependent problem. We analyse the qualitative behavior of the flow using tools of bifurcation theory. The main result is a Hopf bifurcation theorem with -symmetry.
Let Ω be a bounded domain in with smooth boundary ∂Ω and let L denote a second order linear elliptic differential operator and a mapping from into itself with compact inverse, with eigenvalues , each repeated according to its multiplicity, 0 < λ1 < λ2 < λ3 ≤ ... ≤ λi ≤ ... → ∞. We consider a semilinear elliptic Dirichlet problem in Ω, u=0 on ∂ Ω. We assume that , and f is generated by and . We show a relation between the multiplicity of solutions and source terms in the equation....
We consider the -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite and investigate the limit problem as .
We prove the existence of a principal eigenvalue associated to the ∞-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.
We prove the existence of a principal eigenvalue associated to the ∞-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.
We show that the study of the principal spectrum of a linear nonautonomous parabolic PDE of second order on a bounded domain, with the Dirichlet or Neumann boundary conditions, reduces to the investigation of the spectrum of the linear nonautonomous ODE v̇ = a(t)v.
We consider the pseudo--laplacian, an anisotropic version of the -laplacian operator for . We study relevant properties of its first eigenfunction for finite and the limit problem as .
We consider the pseudo-p-Laplacian, an anisotropic version of the p-Laplacian operator for . We study relevant properties of its first eigenfunction for finite p and the limit problem as p → ∞.
We show that the ``radiation field'' introduced by F.G. Friedlander, mapping Cauchy data for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic manifold. The underlying canonical relation is associated to a ``sojourn time'' or ``Busemann function'' for geodesics. As a consequence we obtain some information about the high frequency behavior of the scattering...