scholarly journals Some Steiner Symmetry Results in Overdetermined Boundary Value Problem

2011 ◽  
Vol 01 (06) ◽  
pp. 340-344
Author(s):  
Zhongbo Fang ◽  
Anna Wang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Overdetermined Boundary Value Problem

Recovery of harmonic functions from partial boundary data respecting internal pointwise values

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Juliette Leblond ◽  
Dmitry Ponomarev
Keyword(s):  
Boundary Value Problem ◽  
Connected Domain ◽  
Harmonic Functions ◽  
Boundary Data ◽  
Boundary Value ◽  
Lipschitz Boundary ◽  
Simply Connected Domain ◽  
Simply Connected ◽  
Overdetermined Boundary Value Problem

Abstract We consider partially overdetermined boundary-value problem for Laplace PDE in a planar simply connected domain with Lipschitz boundary

scholarly journals Interpolating estimates with applications to some quantitative symmetry results

2022 ◽  
Vol 5 (1) ◽  
pp. 1-21
Author(s):  
Rolando Magnanini ◽  
◽  
Giorgio Poggesi ◽  
Keyword(s):  
Boundary Value Problem ◽  
General Class ◽  
Riesz Potential ◽  
Boundary Value ◽  
Lipschitz Domains ◽  
Soap Bubble ◽  
New Approach ◽  
Pointwise Bound ◽  
Overdetermined Boundary Value Problem

<abstract><p>We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $ L^p $ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient. The estimates hold for a general class of domains, including, e.g., Lipschitz domains. All the constants involved can be explicitly computed. As an application, we show how to use these estimates to obtain stability for Alexandrov's Soap Bubble Theorem and Serrin's overdetermined boundary value problem. The new approach results in several novelties and benefits for these problems.</p></abstract>

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