An Elementary Partial Regularity Proof for Vector-Valued Obstacle Problems.
An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential.
An Existence Theorem for Class of Non-Coercive Optimization and Variational Problems.
Analysis of total variation flow and its finite element approximations
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter , and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since our...
Analysis of total variation flow and its finite element approximations
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε, see (1.7)) and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since...
Analytical treatment of generalized Burgers-Huxley equation by homotopy analysis method.
Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions
Anti-symmetric hamiltonians (II) : variational resolutions for Navier-Stokes and other nonlinear evolutions
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Applications of a max-min principle
Approximations of Sobolev maps between an open set and an Euclidean sphere, boundary data, and singularities.
A-quasiconvexity : weak-star convergence and the gap
Asymmetric heteroclinic double layers
Let be a non-negative function of class from to , which vanishes exactly at two points and . Let be the set of functions of a real variable which tend to at and to at and whose one dimensional energyis finite. Assume that there exist two isolated minimizers and of the energy over . Under a mild coercivity condition on the potential and a generic spectral condition on the linearization of the one-dimensional Euler–Lagrange operator at and , it is possible to prove...
Asymmetric heteroclinic double layers
Let W be a non-negative function of class C3 from to , which vanishes exactly at two points a and b. Let S1(a, b) be the set of functions of a real variable which tend to a at -∞ and to b at +∞ and whose one dimensional energy is finite. Assume that there exist two isolated minimizers z+ and z- of the energy E1 over S1(a, b). Under a mild coercivity condition on the potential W and a generic spectral condition on the linearization of the one-dimensional Euler–Lagrange operator at z+ and...
Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle.
Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential
We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].
Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential
The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential , is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.
Blow-up solutions of the self-dual Chern–Simons–Higgs vortex equation
Boundary value problems for non-parametric surfaces of prescribed mean curvature