Uniqueness of {\sigma}-regular solutions of quasilinear elliptic problems

We study the uniqueness problem of $\sigma$-regular solution of the equation, -\Delta_p u+ \abs u^{q-1}u =h \quad on\quad \RN, where $q>p-1>0.$ and $N> p.$ Other coercive type equations associated to more general differential operators are also investigated. Our uniqueness results hold for equations associated to the mean curvature type operators as well as for more general quasilinear subelliptic operators.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1209.190

Entire solutions of quasilinear elliptic systems on Carnot Groups

We prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems. The results are new even in the Euclidean setting.Comment: 21 pages submitte

Quasilinear elliptic systems in divergence form associated to general nonlinearities

The paper is concerned with a priori estimates of positive solutions of quasilinear elliptic equations inequalities in a open set of R^N associated to general continuous nonlinearities satisfying a a local assumption near zero. As a consequence, in the case Omega subset R^N , we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed

On some multicomponent quasilinear elliptic systems

The paper contains some Liouville theorems for second order multicomponent quasilinear elliptic systems of equations or inequalities in RN associated to general nonlinearities. No assumptions on the behaviour of the solutions at infinity are assumed

Viscous resuspension of non-Brownian particles: determination of the concentration profiles and particle normal stresses

We perform local measurements of both the shear rate and the particle fraction to study viscous resuspension in non-Brownian suspensions. A suspension of PMMA spherical particles dispersed in a lighter Newtonian fluid (Triton X100) is sheared in a vertical Couette cell. The vertical profiles of the particle volume fraction are measured for Shields numbers ranging from 10 −3 to 1, and the variation in the particle normal stress in the vorticity direction of the particle fraction is deduced

Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups

AbstractVariants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented

ENTIRE SOLUTIONS OF CERTAIN FOURTH ORDER ELLIPTIC PROBLEMS AND RELATED INEQUALITIES

We study distributional solutions of semilinear biharmonic equations of the type ∆2u+f(u)=0 onRN, where f is a continuous function satisfying f(t)t ≥ c|t|q+1 for all t ∈ R with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy-Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions

Representation formulae of solutions of second order elliptic inequalities

2noWe prove various representation formulae of solutions of second order dierential inequalities on RN . As an outcome we obtain positivity results of the solutions of ≠Lu Ø 0, where L is a general second order elliptic operator in divergence form. Results of this type are very useful for studying related Liouville theorems of second order semilinear inequalities.partially_openembargoed_20210915Lorenzo D'Ambrosio ; Enzo MitidieriD'Ambrosio, Lorenzo; Mitidieri, Enz