scholarly journals Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains Application to the Extended Courant Property

2021 ◽  
Vol 30 (3) ◽  
pp. 429-462
Author(s):  
Pierre Bérard ◽  
Bernard Helffer
Keyword(s):  
Level Sets ◽  
Lipschitz Domains

Perfect level sets in many directions

1986 ◽  
Vol 12 (1) ◽  
pp. 176
Author(s):  
Malý
Keyword(s):  
Level Sets

LEVEL SETS OF A TYPICAL C n FUNCTION

1998 ◽  
Vol 24 (1) ◽  
pp. 83
Author(s):  
Darji ◽  
Morayne
Keyword(s):  
Level Sets

scholarly journals On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems

2021 ◽  
Author(s):  
Pier Domenico Lamberti ◽  
Luigi Provenzano
Keyword(s):  
Fourier Series ◽  
Dirichlet Problem ◽  
Lipschitz Domain ◽  
Spectral Properties ◽  
Explicit Representation ◽  
Lipschitz Domains ◽  
Dirichlet Problems ◽  
Trace Space ◽  
In Series ◽  
Definition Of

AbstractWe consider the problem of describing the traces of functions in $$H^2(\Omega )$$ H 2 ( Ω ) on the boundary of a Lipschitz domain $$\Omega $$ Ω of $$\mathbb R^N$$ R N , $$N\ge 2$$ N ≥ 2 . We provide a definition of those spaces, in particular of $$H^{\frac{3}{2}}(\partial \Omega )$$ H 3 2 ( ∂ Ω ) , by means of Fourier series associated with the eigenfunctions of new multi-parameter biharmonic Steklov problems which we introduce with this specific purpose. These definitions coincide with the classical ones when the domain is smooth. Our spaces allow to represent in series the solutions to the biharmonic Dirichlet problem. Moreover, a few spectral properties of the multi-parameter biharmonic Steklov problems are considered, as well as explicit examples. Our approach is similar to that developed by G. Auchmuty for the space $$H^1(\Omega )$$ H 1 ( Ω ) , based on the classical second order Steklov problem.

scholarly journals Gradient-Free Tracking of Unsteady Environmental Level Sets in Dynamic Environments by a Nonholonomic Robot

2020 ◽  
Vol 53 (2) ◽  
pp. 9256-9261
Author(s):  
Alexey Matveev ◽  
Alexander Kapitonov ◽  
Ivan Berman ◽  
Valerii Chernov
Keyword(s):  
Level Sets ◽  
Dynamic Environments ◽  
Environmental Level

scholarly journals Feature Level-Sets: Generalizing Iso-Surfaces to Multi-Variate Data

2020 ◽  
Vol 26 (2) ◽  
pp. 1308-1319 ◽  
Author(s):  
Jochen Jankowai ◽  
Ingrid Hotz
Keyword(s):  
Level Sets
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