-Laplacian equations in with critical growth.
Necessary conditions of existence for an elliptic equation with source term and measure data involving -Laplacian.
Néel and Cross-Tie wall energies for planar micromagnetic configurations
We study a two-dimensional model for micromagnetics, which consists in an energy functional over -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....
Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations
We study a two-dimensional model for micromagnetics, which consists in an energy functional over S2-valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....
Nehari's problem and competing species systems
Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
New a priori estimates for -nonlinear elliptic systems with strong nonlinearities in the gradient, .
New estimates for div-curl products and very weak solutions of PDEs
New exact solutions to the nonautonomous Liouville equation.
New isoperimetric estimates for solutions to Monge-Ampère equations
New results on the Burgers and the linear heat equations in unbounded domains.
We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 +∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given.
New solutions of equations on
Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter
Non-Divergence From Operators and Variations on Yau's Explosion Criterion.
Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations
Nonexistence of entire positive solution for a conformal -Hessian inequality
In this paper, we study the nonexistence of entire positive solution for a conformal -Hessian inequality in via the method of proof by contradiction.
Nonexistence of local solutions to semilinear partial differential inequalities
Nonexistence of positive singular solutions for a class of semilinear elliptic systems.
Nonexistence of solutions for quasilinear elliptic equations with -growth in the gradient.
Nonexistence results of solutions to systems of semilinear differential inequalities on the Heisenberg group.