A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
A very singular solution for the dual porous medium equation and the asymptotic behaviour of general solutions.
A viscosity solution method for Shape-From-Shading without image boundary data
In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884],...
A W 2, 2 Bound for a Class of Elliptic Equations in Nondivergence Form with Rough Coefficients.
A W1,p-Estimate for Solutions to Mixed Boundary Value Problems for Second Order Elliptic Differential Equtions.
A waiting time phenomenon for thin film equations
A wave equation associated with mixed nonhomogeneous conditions: The compactness and connectivity of weak solution set.
A wave equation with a Dirac distribution.
A wave equation with discontinuous time delay.
A wavelet based space-time adaptive numerical method for partial differential equations
A wavelet Galerkin method applied to partial differential equations with variable coefficients.
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains
A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.
A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces
We shall prove a weak comparison principle for quasilinear elliptic operators that includes the negative -Laplace operator, where satisfies certain conditions frequently seen in the research of quasilinear elliptic operators. In our result, it is characteristic that functions which are compared belong to different spaces.
A weak maximum principle and estimates of for nonlinear degenerate elliptic equations
A weakly over-penalized symmetric interior penalty method.
A Weighted Eigenvalue Problems Driven by both -Harmonic and -Biharmonic Operators
The existence of at least one non-decreasing sequence of positive eigenvalues for the problem driven by both -Harmonic and -biharmonic operators is proved by applying a local minimization and the theory of the generalized Lebesgue-Sobolev spaces and .
A weighted isoperimetric inequality and applications to symmetrization.
A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media
In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution of an elliptic equation, that we write , can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the method to...
A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion
In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.