Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients
Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy
For external magnetic field hex ≤ Cε–α, we prove that a Meissner state solution for the Chern-Simons-Higgs functional exists. Furthermore, if the solution is stable among all vortexless solutions, then it is unique.
Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the ∞-Laplacian.
En esta nota estimamos la tasa máxima de crecimiento en la frontera de las soluciones de viscosidad de -Δ∞u + λ|u|m-1u = f en Ω (λ > 0, m > 3).De hecho, mostramos que sólo hay una única tasa de explosión en la frontera para esas soluciones explosivas. También obtenemos una versión del Teorema de Liouville para el caso Ω = RN.
Uniqueness of the Cauchy problem for a second order operator
Uniqueness of the Cauchy problem for convolution equations.
Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov–Poisson system
Uniqueness of the Multi-Dimensional Inverse Scattering Problem for Time Dependent Potentials.
Uniqueness of the Rothe method for the Burgers equation with piecewise continuous initial data
Uniqueness of the Solution of a Semilinear Boundary Value Problem.
Uniqueness of the solution of the Cauchy problem to some equations of nonstationary filtration
Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games
Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.
We show the uniqueness of the very singular self-similar solution of the equationut - Δ pum + uq = 0.The result is carried out by studying the stationary associate equation and by introducing a suitable change of unknown. That allows to assume the zero-order perturbation term in the new equation to be monotone increasing. A careful study of the behaviour of solutions near the boundary of their support is also used in order to prove the main result.
Uniqueness of weak solution for nonlinear elliptic equations in divergence form.
Uniqueness of weak solutions of the Navier-Stokes equations
Consider the Navier-Stokes equation with the initial data . Let and be two weak solutions with the same initial value . If satisfies the usual energy inequality and if where is the multiplier space, then we have .
Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes model with a logistic source
We prove a uniqueness result of weak solutions to the Cauchy problem of a Keller-Segel-Navier-Stokes system with a logistic term.
Uniqueness results for elliptic problems with singular data.
Uniqueness results for some PDEs
Existence of solutions to many kinds of PDEs can be proved by using a fixed point argument or an iterative argument in some Banach space. This usually yields uniqueness in the same Banach space where the fixed point is performed. We give here two methods to prove uniqueness in a more natural class. The first one is based on proving some estimates in a less regular space. The second one is based on a duality argument. In this paper, we present some results obtained in collaboration with Pierre-Louis...
Uniqueness results for the Minkowski problem extended to hedgehogs
The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.
Uniqueness theorems for steady, compressible, heat-conducting fluids: exterior domains
Si fornisce un teorema di unicità per moti stazionari regolari di fluidi compressibili, viscosi, termicamente conduttori, svolgentisi in regioni esterne a domini compatti della spazio fisico.
Uniqueness/nonuniqueness for nonnegative solutions of a class of second-order parabolic equations