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A Hörmander-type spectral multiplier theorem for operators without heat kernel

Sönke Blunck (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hörmander’s famous Fourier multiplier theorem ensures the L p -boundedness of F ( - Δ ℝ D ) whenever F ∈ ℋ ( s ) for some s > D 2 , where we denote by ℋ ( s ) the set of functions satisfying the Hörmander condition for s derivatives. Spectral multiplier theorems are extensions of this result to more general operators A ≥ 0 and yield the L p -boundedness of F ( A ) provided F ∈ ℋ ( s ) for some s sufficiently large. The harmonic oscillator A = - Δ ℝ + x 2 shows that in general s > D 2 is not sufficient even if A has a heat kernel satisfying gaussian estimates. In this paper,...

On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points

Nguyen Manh Hung, Hoang Viet Long, Nguyen Thi Kim Son (2013)

Applications of Mathematics

In this paper, for the second initial boundary value problem for Schrödinger systems, we obtain a performance of generalized solutions in a neighborhood of conical points on the boundary of the base of infinite cylinders. The main result are asymptotic formulas for generalized solutions in case the associated spectrum problem has more than one eigenvalue in the strip considered.

On the Paneitz energy on standard three sphere

Paul Yang, Meijun Zhu (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We prove that the Paneitz energy on the standard three-sphere S 3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.

On the Paneitz energy on standard three sphere

Paul Yang, Meijun Zhu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.

Partial regularity for anisotropic functionals of higher order

Menita Carozza, Antonia Passarelli di Napoli (2007)

ESAIM: Control, Optimisation and Calculus of Variations


We prove a C k , α partial regularity result for local minimizers of variational integrals of the type I ( u ) = ∫ Ω f ( D k u ( x ) ) d x , assuming that the integrand f satisfies (p,q) growth conditions.


Some solutions for a class of singular equations

Abdullah Altin, Ayşegül Erençin (2004)

Czechoslovak Mathematical Journal

In this paper we obtain all solutions which depend only on r for a class of partial differential equations of higher order with singular coefficients.

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