Positive solutions of quasilinear elliptic systems with strong dependence on the gradient.
Prescribing -curvature on higher dimensional spheres
We study the problem of prescribing a fourth order conformal invariant on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of such critical points at infinity, we prove some existence results.
Problèmes aux limites non linéaires, non coercifs
Quasilinear Elliptic Operations and Weak Solutions of the Euler Equation.
Regularity in elliptic free boundary problems. II. Equations of higher order
Saddle-point problems in partial differential equations and applications to linear quadratic differential games
Solutions of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents
Some solutions are obtained for a class of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents by variational methods and some analysis techniques.
Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations
This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in , on ∂Ω in the Sobolev space , where L is any selfadjoint strongly elliptic linear differential operator of order 2m. Using both topological degree arguments and minimax methods we obtain existence and multiplicity results for the above problem.
Some regularity results for a family of variational inequalities
Strong ellipticity of boundary integral operators.
Strongly elliptic linear operators without coercive quadratic forms I. Constant coefficient operators and forms
A family of linear homogeneous 4th order elliptic differential operators with real constant coefficients, and bounded nonsmooth convex domains are constructed in so that the have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces .
Strongly nonlinear problem of infinite order with data.
Sul problema della goccia appoggiata
Sul problema di Dirichlet in un cono per l’equazione
Sur la méthode variationnelle pour les équations aux dérivées partielles non linéaires du type elliptique; l'existence et la régularité des solutions
Sur la régularité des solutions faibles des équations elliptiques non-linéaires
Sur la régularité des solutions variationnelles des équations elliptiques non-linéaires d’ordre en deux dimensions
Sur l’appartenance dans la classe des solutions variationnelles des équations elliptiques non-linéaires de l’ordre en deux dimensions (Communication préalable)
Symmetry breaking in the minimization of the first eigenvalue for the composite clamped punctured disk
Let D₀=x∈ ℝ²: 0<|x|<1 be the unit punctured disk. We consider the first eigenvalue λ₁(ρ ) of the problem Δ² u =λ ρ u in D₀ with Dirichlet boundary condition, where ρ is an arbitrary function that takes only two given values 0 < α < β and is subject to the constraint for a fixed 0 < γ < |D₀|. We will be concerned with the minimization problem ρ ↦ λ₁(ρ). We show that, under suitable conditions on α, β and γ, the minimizer does not inherit the radial symmetry of the domain.
The obstacle problem for the biharmonic operator