Sharp singular Adams inequalities in high order Sobolev spaces
By Nguyen Huong Lam, G. Lu. 2011
51 citations recorded by the source corpus.
In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in $\mathbb{R}^{n}$. Using this we prove a sharp singular Adams inequality in high order Sobolev spaces in bounded domain at critical case. Then we prove sharp singular Adams inequalities for high order derivatives on unbounded domains. Our results extend the singular Moser-Trudinger inequalities of first order in \cite{Ad2, R, LR, AdY} to the higher order Sobolev spaces $W^{m,\frac{n}{m}}$ and the results of \cite{RS} on Adams type inequalities in unbounded domains to singular case. Our singular Adams inequality on $W^{2,2}(\mathbb{R}^{4})$ with standard Sobolev norm at the critical case settles a unsolved question remained in \cite{Y}.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/ef46e7584b07f9a4f638fdbd1364f181dcceb868
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, methodology): “As a result, we will avoid using the deep comparison principle of Talenti [50] and Trombetti and Vázquez [53] to establish the Adams inequality on finite domains by as done in [48] and [29,30].”
- Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities (2015, methodology): “In fact, using a new idea that one can write a smooth function as a convolution of a (Riesz) potential with its derivatives, and then one can use the symmetrization for this convolution, instead of the symmetrization of the higher order derivatives, Adams proved the following inequality with boundar”
- Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, methodology): “Adams inequality has been recently generalized to unbounded domains on high order Sobolev spaces W m, n m (R n ) for any even order by Ruf–Sani [66] and to any odd order by the authors [42] [47].”