Remarks on Parameter Identification. I.
Remarks on the theory of elasticity
In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some -norm of the gradient with is controlled...
Remarks on the Yamabe problem and the Palais-Smale condition
Renormalized solutions of elliptic equations with general measure data
Saddle point theorem and Fredholm alternative
Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential
We consider a singularly perturbed elliptic equation on , , where for any . The singularly perturbed problem has corresponding limiting problems on , . Berestycki-Lions found almost necessary and sufficient conditions on nonlinearity for existence of a solution of the limiting problem. There have been endeavors to construct solutions of the singularly perturbed problem concentrating around structurally stable critical points of potential under possibly general conditions on . In...
Semilinear Elliptic Equations on Unbounded Domains.
Smoothness and analyticity of free boundaries in variational inequalities
Solitary waves for Maxwell-Schrödinger equations.
Solution of parabolic equations by means of Lyapunov functionals.
Solutions to elliptic systems of Hamiltonian type in .
Some critical point theorems and applications to semilinear elliptic partial differential equations
Some geometric aspects of the calculus of variations in several independent variables
This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.
Some Linear Elliptic Selfsimilar Equations with Whirl-Like Solutions.
Some relatively new techniques for nonlinear problems.
Space-time variational saddle point formulations of Stokes and Navier–Stokes equations
The instationary Stokes and Navier−Stokes equations are considered in a simultaneously space-time variational saddle point formulation, so involving both velocities u and pressure p. For the instationary Stokes problem, it is shown that the corresponding operator is a boundedly invertible linear mapping between H1 and H'2, both Hilbert spaces H1 and H2 being Cartesian products of (intersections of) Bochner spaces, or duals of those. Based on these results, the operator that corresponds to the Navier−Stokes...
Stability of peakons for the generalized Camassa-Holm equation.
Stability of solitary waves for a system of nonlinear Schrödinger equations with three wave interaction
Stability of solitary waves for derivative nonlinear Schrödinger equation
Stability of solutions for an abstract Dirichlet problem
We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.