A note on harmonic maps between surfaces
A note on quasilinear elliptic eigenvalue problems.
A note on Ricci flow and optimal transportation
We describe a new link between Perelman’s monotonicity formula for the reduced volume and ideas from optimal transport theory.
A note on strong resonance problems for -Laplacian.
A note on the existence of two nontrivial solutions of a resonance problem.
A numerically based investigation on the symmetry breaking and asymptotic behavior of the ground states to the -Hénon equation.
A pair hamiltonian model of a non-ideal Boson gas
A partial regularity result for a class of stationary Yang-Mills in high dimension.
We prove, for arbitrary dimension of the base n greater than or equal to 4, stationary Yang-Mills Fields satisfying Borne approximability property are regular apart from a closed subset of the base having zero (n-4)- Hausdorff measure.
A perspective on the contributions of Alan C. Lazer to critical point theory.
A Pertubation Theorem for Surfaces of Constant Mean Curvature.
A perturbation result concerning a second solution to the Dirichlet problem for the equation of prescribed mean curvature.
A positive solution for an asymptotically linear elliptic problem on autonomous at infinity
In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on . The main difficulties to overcome are the lack of a priori bounds for Palais–Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be used in order...
A positive solution for an asymptotically linear elliptic problem on autonomous at infinity
In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on . The main difficulties to overcome are the lack of a priori bounds for Palais–Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be used in order...
A posteriori error analysis for parabolic variational inequalities
Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain with a continuous piecewise smooth obstacle. We formulate a fully discrete method by using piecewise linear finite elements in space and the backward Euler method in time. We define an a posteriori error estimator and show that it gives an upper bound for the error in L2(0,T;H1(Ω)). The error estimator is localized in the sense that the size of the elliptic residual...
A principle of linearization in theory of stability of solutions of variational inequalities
It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
A priori bounds and renormalized Morse indices of solutions of an elliptic system
A priori estimates for harmonic mappings.
A problem of minimization with relaxed energy
A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation
The Witten deformation is an analytic method proposed by Witten which, given a Morse function on a smooth compact manifold , allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities...
A proximal regularization of the steepest descent method in Riemannian manifold.