Solution of a Dirichlet problem in a crescent-shaped domain
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We present a solution of a Dirichlet problem for the Laplace equation in a crescentshaped domain and apply this solution to some stationary problems of heat conduction, electrostatics, and the theory of elasticity.
KeywordsStatistical Physic Heat Conduction Stationary Problem Dirichlet Problem Laplace Equation
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- 1.V. I. Vlasov and A. P. Prudnikov, “Asymptotics of the solutions of some problems for the Laplace equation with deformation of a domain,” in: Modern Problems of Mathematics, Vol. 20 [in Russian] (Advances in Science and Engineering, VINITI, Academy of Sciences of the USSR), Moscow (1982), pp. 3–36.Google Scholar
- 2.Ya. S. Uflyand, Bipolar Coordinates in the Theory of Elasticity [in Russian], GITTL, Moscow-Leningrad (1950).Google Scholar
- 3.Hu Hai-Chang, “Torsion of prisms bounded by two intersecting circular cylinders,” Acta Phys. Sinica,9, No. 4, 238–254 (1953).Google Scholar
- 4.T. H. Gronwall, “On the influence of keyways of the stress distribution in cylindrical shafts,” Trans. Am. Math. Soc.,20, No. 3, 234–244 (1919).Google Scholar
- 5.S. P. Timoshenko, Theory of Elasticity, McGraw-Hill, New York (1934).Google Scholar
- 6.I. S. Sokolnikoff and E. S. Sokolnikoff, “Torsion of regions bounded by circular arcs,” Bull. Am. Math. Soc.,44, No. 3, 384–387 (1938).Google Scholar
- 7.Ya. I. Burak, Some Problems of Torsion in the Bending of Prismatic Rods [in Ukrainian], Vid. Akad. Nauk UkrRSR, Kiev (1959).Google Scholar