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Abstract
A symmetry problem is solved. A new method is used. The idea of this methodis to reduce to a contradiction the PDE and the over-determined boundary data on the boundary.The new method allows one to solve other symmetry problems.
Highlights
Symmetry problems for PDE were studied in many publications by many authors, see, for example, [1]
R3, S is the boundary of D, N is the unit normal to S, pointing out of D, uN is the normal derivative of u on S, D = R3 \ D, S2 is the unit sphere in R3, Jn(r) is the Bessel function regular at r
Let us formulate the symmetry problem studied in this paper
Summary
Symmetry problems for PDE were studied in many publications by many authors, see, for example, [1]. In this paper a new method is given for a study of symmetry problems for PDE. R3, S is the boundary of D, N is the unit normal to S, pointing out of D, uN is the normal derivative of u on S, D = R3 \ D, S2 is the unit sphere in R3, Jn(r) is the Bessel function regular at r
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