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On a functional connected to the laplacian in a family of punctured regular polygons in ℝ2

Author

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  • A. R. Aithal

    (University of Mumbai)

  • Acushla Sarswat

    (University of Mumbai)

Abstract

Let p1 and p0 be closed, regular, convex, concentric polygons having n sides in ℝ2 such that the circumradius of p0 is strictly less than the inradius of p1. We fix p1 and vary p0 by rotating it about its center. Let Ω be the interior of p1 p0. Let u be the solution of the stationary problem −Δu = 1 in Ω vanishing on the boundary. We show that the associated Dirichlet energy functional J(Ω) attains its extremum values when the axes of symmetry of p0 coincide with those of p1.

Suggested Citation

  • A. R. Aithal & Acushla Sarswat, 2014. "On a functional connected to the laplacian in a family of punctured regular polygons in ℝ2," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(6), pages 861-874, December.
    • Handle: RePEc:spr:indpam:v:45:y:2014:i:6:d:10.1007_s13226-014-0094-3
    DOI: 10.1007/s13226-014-0094-3
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