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Symmetry of an integral equation with Bessel potential in ℝn+
-
Boqiang Lv
and
Ran Zhuo
Published/Copyright:
May 15, 2013
Abstract.
We investigate an integral equation with Bessel potential
in ℝn+ and prove that every positive solution of the integral equation
is rotationally symmetric about some line parallel to the 
-axis.
Furthermore, we consider an overdetermined problem of the same integral equation in a cylinder type domain 
and obtain the
symmetry of both domains and solutions, where 
is a bounded domain with 
.
Keywords: Integral equation; Bessel potential; moving planes in integral forms; symmetry; overdetermined problem; cylinder type domain; half space
Received: 2012-05-18
Revised: 2013-01-13
Accepted: 2013-03-27
Published Online: 2013-05-15
Published in Print: 2013-05-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Integral equation;
Bessel potential;
moving planes in integral forms;
symmetry;
overdetermined problem;
cylinder type domain;
half space
Articles in the same Issue
- Masthead
- Fixed points of asymptotically regular mappings in complex-valued metric spaces
- Coverings of internal groupoids and crossed modules in the category of groups with operations
- A new study on almost increasing and quasi-monotone sequences
- On precompact sets in spaces Cc(X)
- Weighted boundedness for Toeplitz type operators related to Riesz transforms of the Schrödinger operator
- Sums of absolutely nonmeasurable functions
- Symmetry of an integral equation with Bessel potential in ℝn+
- Spanier spaces and the covering theory of non-homotopically path Hausdorff spaces
- On the maximal operator of Marcinkiewicz–Fejér means of the two-dimensional Walsh–Kaczmarz system
- Hofer type geometry on the space of Legendrian submanifolds of a contact manifold
- Initial problems for hyperbolic functional differential systems
- Approximation by complex q-Bernstein–Schurer operators in compact disks
- On some properties of conjugate trigonometric Fourier series
