JournalsaihpcVol. 31, No. 2pp. 297–314

On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form

  • Michinori Ishiwata

    Department of Industrial System, Faculty of Symbiotic Systems Science, Fukushima University, Kanayagawa, Fukushima, 960-1296, Japan

  • Makoto Nakamura

    Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

  • Hidemitsu Wadade

    Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan
On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form cover
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Abstract

In this article, we establish the weighted Trudinger–Moser inequality of the scaling invariant form including its best constant and prove the existence of a maximizer for the associated variational problem. The non-singular case was treated by Adachi and Tanaka (1999) [1] and the existence of a maximizer is a new result even for the non-singular case. We also discuss the relation between the best constants of the weighted Trudinger–Moser inequality and the Caffarelli–Kohn–Nirenberg inequality in the asymptotic sense.

Cite this article

Michinori Ishiwata, Makoto Nakamura, Hidemitsu Wadade, On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 2, pp. 297–314

DOI 10.1016/J.ANIHPC.2013.03.004