Международная конференция «Математические и информационные технологии, MIT-2011»
(IX конференция «Вычислительные и информационные технологии в науке,
технике и образовании») № гос. регистрации 0321102644, ISBN 978-5-905569-02-9

Врнячка Баня, Сербия, 27–31 августа 2011 г.

Будва, Черногория, 31 августа – 5 сентября 2011 г.

Mateljevic M.  

Isoperimetric inequality and capacity; Thomson's theorem on equilibrium potential

We  investigate   connections between mathematical potential theory and electrodynamics.
For example,  we consider  Thomson's theorem related to equilibrium potential from mathematical point of view and find motivation in physics for mathematical potential theory  and vice versa.
We also discuss versions of isoperimetric inequality related to capacity and electrostatic capacity.  We consider  inequalities between geometric quantities as perimeter, average diameter, area and capacity. In particular,  we extend result that among all domains with given volume  of the holes the domain bounded by two concentric spheres gives the smallest value $cap_F(K, D)$. Our investigation is also involved by connection between isoperimetric
inequality, capacity, modulus of family of curves and Thomson's theorem related to equilibrium potential.


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