On the Liouville property for sublaplacians
On the method of fictitious domains for a fourth order quasilinear elliptic equation. (Sur la méthode des domaines fictifs pour une équation elliptique quasilinéaire du quatrième ordre.)
On the Newton-Kantorovich theorem and nonlinear finite element methods
Using a weaker version of the Newton-Kantorovich theorem, we provide a discretization result to find finite element solutions of elliptic boundary value problems. Our hypotheses are weaker and under the same computational cost lead to finer estimates on the distances involved and a more precise information on the location of the solution than before.
On the nonlinear Neumann problem with critical and supercritical nonlinearities [Book]
On the number of positive solutions of some weakly nonlinear equations on annular regions.
On the numerical solution of some semilinear elliptic problems.
On the optimal control of nonresonant elliptic equations
On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding
We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ in Ω, ⎨ ⎩ on crtial ∂Ω and we show that the first one μ₁(λ) is simple and isolated; we also prove some results about variations of the density ϱ and the continuity with respect to the parameter λ.
On the radially symmetric solutions of a BVP for a class of nonlinear elliptic partial differential equations.
On the range of nonlinear operators with linear asymptotes which are not invertible
On the regularity of solutions to a nonvariational elliptic equation
On the regularity of the minimizer of a functional with exponential growth
Minimizers of a functional with exponential growth are shown to be smooth. The techniques developed for power growth are not applicable to the exponential case.
On the role of boundary conditions for CIP stabilization of higher order finite elements.
On the singular limit in a phase field model of phase transitions
On the solution of a generalized system of von Kármán equations
A nonlinear system of equations generalizing von Kármán equations is studied. The existence of a solution is proved and the relation between the solutions of the considered system and the solutions of von Kármán system is studied. The system considered is derived in a former paper by Lepig under the assumption of a nonlinear relation between the intensity of stresses and deformations in the constitutive law.
On the solution of the Liouville equation over a rectangle.
On the solvability of monge-ampere type equations in non-uniformly convex domains.
On the solvability of nonlinear elliptic equations in Sobolev spaces
We consider the existence of solutions of the system (*) , l = 1,...,k,
On the solvability of semilinear elliptic equation via an associated eigenvaule problem.
On the solvability of von Kármán equations