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arXiv · 1905.07759

On an effect of inhomogeneous constraints for a maximizing problem of the Sobolev embedding associated with the space of bounded variation

Michinori Ishiwata·Hidemitsu Wadade
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Abstract

In this paper, we consider a maximizing problem associated with the Sobolev type embedding on the space of bounded variation. We show that, although the maximizing problem suffers from both of the non-compactness of vanishing and concentrating phenomena, there exists a maximizer for some range of the exponents. Furthermore, we show that any maximizer must be given by a characteristic function on a ball.

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Michinori Ishiwata, Hidemitsu Wadade. 2019-05-19. On an effect of inhomogeneous constraints for a maximizing problem of the Sobolev embedding associated with the space of bounded variation. https://arxiv.org/abs/1905.07759

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