A p-Laplacian Approximation for Some Mass Optimization by Bouchitte G., Buttazzo G., De Pascale L.

By Bouchitte G., Buttazzo G., De Pascale L.

We convey that the matter of discovering the easiest mass distribution, either in conductivity and elasticity situations, should be approximated by way of recommendations of a p-Laplace equation, as p→+S. This turns out to supply a range criterion whilst the optimum options are nonunique.

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Just as Flatlanders on a sphere could travel the straightest possible line in any direction and everltually return to their starting point, so (Einstein suggested) if a spaceship left the earth and traveled far enough in any one direction, it would eventually return to the earth. If a Flatlander started to paint the surface of the sphere on which he lived, extending the paint outward in ever widening circles, he would reach a halfway point at which the circles would begin to diminish, with himself on the inside, and eventually he would paint himself into a spot.

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