Journal
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume 105, Issue 3, Pages 1897-1935Publisher
WILEY
DOI: 10.1112/jlms.12549
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Funding
- INdAM-GNAMPA [PRIN 2017JPCAPN]
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We establish Moser-Trudinger-type inequalities in the presence of a logarithmic convolution potential when the domain is a ball or the entire space R2. Moreover, we characterize critical nonlinear growth rates for these inequalities to hold and for the existence of corresponding extremal functions. In addition, we show that extremal functions satisfy corresponding Euler-Lagrange equations, and we derive general symmetry and uniqueness results for solutions of these equations.
We establish Moser-Trudinger-type inequalities in the presence of a logarithmic convolution potential when the domain is a ball or the entire space R2$\mathbb {R}<^>2$. Moreover, we characterize critical nonlinear growth rates for these inequalities to hold and for the existence of corresponding extremal functions. In addition, we show that extremal functions satisfy corresponding Euler-Lagrange equations, and we derive general symmetry and uniqueness results for solutions of these equations.
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