Contents
Contingent solutions to the center manifold equation
Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems
A class of quasilinear parabolic systems with quadratic nonlinearities in the gradient is considered. It is assumed that the elliptic operator of a system has variational structure. In the multidimensional case, the behavior of solutions of the Cauchy-Dirichlet problem smooth on a time interval is studied. Smooth extendibility of the solution up to is proved, provided that “normilized local energies” of the solution are uniformly bounded on . For the case where determines the maximal interval...
Continuation of analytic solutions of linear differential equations up to convex conical singularities
Continuation of the connection matrix for singularly perturbed hyperbolic equations
Continuité-Sobolev de certains opérateurs paradifférentiels.
L'objet de ce travail est l'étude de la continuité des opérateurs d'intégrales singulières (au sens de Calderón-Zygmund) sur les espaces de Sobolev Hs. Il complète le travail fondamental de David-Journé [6], concernant le cas s = 0, et ceux de P. G. Lemarié [10] et M. Meyer [11] concernant le cas 0 < s < 1.
Continuity, curvature, and the general covariance of optimal transportation
Continuity Estimates for Solutions to the Prescribed-Curvature Dirichlet Problem.
Continuity for bounded solutions of multiphase Stefan problem
We establish the continuity of bounded local solutions of the equation . Here is any coercive maximal monotone graph in , bounded for bounded values of its argument. The multiphase Stefan problem and the Buckley-Leverett model of two immiscible fluids in a porous medium give rise to such singular equations.
Continuity of attractors
Continuity of attractors for a reaction-diffusion problem with respect to variations of the domain.
Continuity of Minimal Surfaces with Piecewise Smooth Free Boundaries.
Continuity of solutions of a nonlinear elliptic equation
We consider a nonlinear elliptic equation of the form div [a(∇u)] + F[u] = 0 on a domain Ω, subject to a Dirichlet boundary condition tru = φ. We do not assume that the higher order term a satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and φ satisfies a one-sided bounded slope condition, or when ais radial: a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasingl:ℝ+ → ℝ+.
Continuity of solutions of a quasilinear hyperbolic equation with hysteresis
This paper is devoted to the investigation of quasilinear hyperbolic equations of first order with convex and nonconvex hysteresis operator. It is shown that in the nonconvex case the equation, whose nonlinearity is caused by the hysteresis term, has properties analogous to the quasilinear hyperbolic equation of first order. Hysteresis is represented by a functional describing adsorption and desorption on the particles of the substance. An existence result is achieved by using an approximation of...
Continuity of solutions of linear, degenerate elliptic equations
We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.
Continuity of solutions of the porous media equation
Continuity of solutions of uniformly elliptic equations in R2.
Continuity of solutions to a basic problem in the calculus of variations
We study the problem of minimizing over the functions that assume given boundary values on . The lagrangian and the domain are assumed convex. A new type of hypothesis on the boundary function is introduced: thelower (or upper) bounded slope condition. This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary...
Continuity of the Darcy's law in the low-volume fraction limit
Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front sets satisfy some conditions. Thus, it is natural to investigate the topological properties of these operations between spaces of distributions having a wave front set included in a given closed cone Γ of the cotangent space. As discovered by S. Alesker, the pull-back is not continuous for the usual topology on , and the tensor product is not separately continuous. In this paper,...