Electron. J. Differential Equations, Vol. 2019 (2019), No. 105, pp. 1-16.

Sharp Trudinger-Moser inequalities with homogeneous weights

Nguyen Tuan Duy, Le Trung Nghia, Le Long Phi

We investigate sharp Trudinger-Moser type inequalities with the homogeneous weight satisfying a natural curvature-dimension bound condition. Also we study the optimal versions of these inequalities with best constants on both finite and infinite volume domains on Euclidean spaces.

Submitted July 30, 2019. Published September 10, 2019.
Math Subject Classifications: 35A23, 26D15, 46E35, 46E30.
Key Words: Trudinger-Moser inequalities; homogeneous weights; best constants; critical growth; exact growth condition.

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Nguyen Tuan Duy
Department of Fundamental Sciences
University of Finance-Marketing
2/4 Tran Xuan Soan St., Tan Thuan Tay Ward, Dist. 7
Ho Chi Minh City, Vietnam
email: tuanduy2312@gmail.com
Le Trung Nghia
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City, Vietnam
email: letrungnghia@tdtu.edu.vn
Le Long Phi
Institute of Research and Development
Duy Tan University
Da Nang 550000, Vietnam
email: lelongphi@duytan.edu.vn

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