To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
In this article, we study some Kramers–Fokker–Planck operators with a polynomial potential
of degree greater than two having quadratic limiting behaviour. This work provides an accurate global subelliptic estimate for Kramers–Fokker–Planck operators under some conditions imposed on the potential.
We prove Hölder continuous regularity of bounded, uniformly continuous, viscosity solutions of degenerate fully nonlinear equations defined in all of ℝn space. In particular, the result applies also to some operators in Carnot groups.
In Albano, Bove and Mughetti [J. Funct. Anal. 274(10) (2018), 2725–2753]; Bove and Mughetti [Anal. PDE 10(7) (2017), 1613–1635] it was shown that Treves conjecture for the real analytic hypoellipticity of sums of squares operators does not hold. Models were proposed where the critical points causing a non-analytic regularity might be interpreted as strata. We stress that up to now there is no notion of stratum which could replace the original Treves stratum. In the proposed models such ‘strata’ were non-symplectic analytic submanifolds of the characteristic variety. In this note we modify one of those models in such a way that the critical points are a symplectic submanifold of the characteristic variety while still not being a Treves stratum. We show that the operator is analytic hypoelliptic.
We introduce an Almgren frequency function of the sub-
-Laplace equation on the Heisenberg group to establish a doubling estimate under the assumption that the frequency function is locally bounded. From this, we obtain some partial results on unique continuation for the sub-
We establish the multiplicity of positive weak solutions for the quasilinear Dirichlet problem −Lpu + |u|p−2u = h(u) in Ωλ, u = 0 on ∂Ωλ, where Ωλ = λΩ, Ω is a bounded domain in ℝN, λ is a positive parameter, Lpu ≐ Δpu + Δp(u2)u and the nonlinear term h(u) has subcritical growth. We use minimax methods together with the Lyusternik–Schnirelmann category theory to get multiplicity of positive solutions.
Descloux and Geymonat considered a model problem in two-dimensional magnetohydrodynamics and conjectured that the essential spectrum has an explicitly given band structure. This conjecture was recently proved by Faierman, Mennicken, and Möller by reducing the problem to that for a 2×2 block operator matrix. In a subsequent paper Faierman and Mennicken investigated the essential spectrum for the problem arising from a particular type of perturbation of precisely one of the operator entries in the matrix representation cited above of the original problem considered by Descloux and Geymonat. In this paper we extend the results of that work by investigating the essential spectrum for the problem arising from particular types of perturbations of all but one of the aforementioned operators. It remains an open question whether one can perturb the exceptional operator in such a way as to leave the essential spectrum unchanged.
Email your librarian or administrator to recommend adding this to your organisation's collection.