scholarly journals $${\text {VMO}}$$ Spaces Associated with Neumann Laplacian

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Mingming Cao ◽  
Kôzô Yabuta
Keyword(s):  
Neumann Laplacian

Ambarzumyan-type theorem for the impulsive Sturm–Liouville operator

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ran Zhang ◽  
Chuan-Fu Yang
Keyword(s):  
Liouville Operator ◽  
Type Theorem ◽  
Sturm Liouville ◽  
Neumann Laplacian ◽  
Neumann Eigenvalues

AbstractWe prove that if the Neumann eigenvalues of the impulsive Sturm–Liouville operator {-D^{2}+q} in {L^{2}(0,\pi)} coincide with those of the Neumann Laplacian, then {q=0}.

scholarly journals Two weight commutators in the Dirichlet and Neumann Laplacian settings

2019 ◽  
Vol 276 (4) ◽  
pp. 1007-1060 ◽  
Author(s):  
Xuan Thinh Duong ◽  
Irina Holmes ◽  
Ji Li ◽  
Brett D. Wick ◽  
Dongyong Yang
Keyword(s):  
Neumann Laplacian

scholarly journals Sobolev inequalities for fractional Neumann Laplacians on half spaces

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Roberta Musina ◽  
Alexander I. Nazarov
Keyword(s):  
Half Space ◽  
Sobolev Inequalities ◽  
Neumann Laplacian ◽  
Sobolev Constants

Abstract We consider different fractional Neumann Laplacians of order {s\in(0,1)} on domains {\Omega\subset\mathbb{R}^{n}} , namely, the restricted Neumann Laplacian {{(-\Delta_{\Omega}^{N})^{s}_{\mathrm{R}}}} , the semirestricted Neumann Laplacian {{(-\Delta_{\Omega}^{N})^{s}_{\mathrm{Sr}}}} and the spectral Neumann Laplacian {{(-\Delta_{\Omega}^{N})^{s}_{\mathrm{Sp}}}} . In particular, we are interested in the attainability of Sobolev constants for these operators when Ω is a half-space.

scholarly journals Extrema of Low Eigenvalues of the Dirichlet–Neumann Laplacian on a Disk

2010 ◽  
Vol 62 (4) ◽  
pp. 808-826
Author(s):  
Eveline Legendre
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Mixed Boundary Conditions ◽  
First Eigenvalue ◽  
Bounded Number ◽  
Eigenvalues Of The Laplacian ◽  
Neumann Laplacian ◽  
Dirichlet And Neumann Conditions ◽  
Second Eigenvalue

AbstractWe study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet–Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact 1-parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded number of parts on which Dirichlet and Neumann conditions are imposed alternately, the first eigenvalue is maximized by the uniformly distributed partition.

The Neumann Laplacian on Generalized Ridged Domains

1995 ◽  
Vol 176 (1) ◽  
pp. 55-64 ◽  
Author(s):  
David E. Edmunds ◽  
Robert M. Kauffman
Keyword(s):  
Neumann Laplacian

Corrigendum to “Spectral Theory for the Neumann Laplacian on Planar Domains with Horn-Like Ends”

2000 ◽  
Vol 52 (1) ◽  
pp. 119-122
Author(s):  
Julian Edward
Keyword(s):  
Spectral Theory ◽  
Planar Domains ◽  
Neumann Laplacian

AbstractErrors to a previous paper (Canad. J. Math. (2) 49(1997), 232–262) are corrected. A non-standard regularisation of the auxiliary operator A appearing in Mourre theory is used.

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