Displaying similar documents to “Asymptotic behavior of solutions of Schrödinger inequalities on unbounded domains of nilpotent Lie groups”

Asymptotics of sums of subcoercive operators

Nick Dungey, A. ter Elst, Derek Robinson (1999)

Colloquium Mathematicae

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We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel...

Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group

E. Lanconelli, F. Uguzzoni (1998)

Bollettino dell'Unione Matematica Italiana

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In questa nota dimostriamo stime asintotiche ottimali per le soluzioni deboli non negative del problema al contorno - Δ H n ⁢ u = u Q + 2 / Q - 2 ⁢ i ⁢ n ⁢ Ω , u = 0 ⁢  in  ⁢ ∂ ⁡ Ω . - Δ H n è il Laplaciano di Kohn sul gruppo di Heisenberg H n , Ω è un aperto non limitato e Q = 2 ⁢ n + 2 è la dimensione omogenea di H n . Utilizziamo successivamente le stime ottenute per dimostrare un teorema di non esistenza per (*) nel caso in cui Ω sia un semispazio di H n con bordo parallelo al centro del gruppo.

A Paley-Wiener theorem for step two nilpotent Lie groups.

Sundaram Thangavelu (1994)

Revista Matemática Iberoamericana

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It is an interesting open problem to establish Paley-Wiener theorems for general nilpotent Lie groups. The aim of this paper is to prove one such theorem for step two nilpotent Lie groups which is analogous to the Paley-Wiener theorem for the Heisenberg group proved in [4].