Adams type inequalities and related elliptic partial differential equations in dimension four

By Y. Yang. 2011

59 citations recorded by the source corpus.

Motivated by Ruf-Sani's recent work, we prove an Adams type inequality and a singular Adams type inequality in the whole four dimensional Euclidean space. As applications of those inequalities, a class of elliptic partial differential equations are considered. Existence of nontrivial weak solutions and multiplicity results are obtained via the mountain-pass theorem and the Ekeland's variational principle. This is a continuation of our previous work about singular Trudinger-Moser type inequality.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a6a1dff70c85b18f9a49b3d9a1ed01e02ed83533

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Caifeng Zhang
2. Nguyen Huong Lam
3. G. Lu
4. Y. Yang
5. Yong Lin
6. Alexander Grigorʼyan
7. Hanli Tang
8. Federica Sani

In Computational Theory and Mathematics

1. Caifeng Zhang
2. G. Lu
3. Nguyen Huong Lam
4. Y. Yang
5. Alexander Grigorʼyan
6. Yong Lin
7. Federica Sani
8. Hanli Tang

Citations in the corpus

• Sharp singular Adams inequalities in high order Sobolev spaces (2011, methodology): “The result of [47] (stated as Theorem D above) for m being even were also extended recently using the standard Sobolev norm by Yang in the special case n = 4 and m = 2 [58] and by the authors [29] to the case n = 2m for all m being both odd and even.”
• Sharp Adams type inequalities in Sobolev spaces Wm,nm(Rn) for arbitrary integer m (2012, background): “In the special case n = 2m = 4k = 4, the above theorem was proved by Yang in [41].”
• Yamabe type equations on graphs (2016, background): “For related works, we refer the reader to [10,2,25,26] and the references there in.”
• Trudinger–Moser Inequalities in Fractional Sobolev–Slobodeckij Spaces and Multiplicity of Weak Solutions to the Fractional-Laplacian Equation (2018, methodology): “Motivated by [3, 17, 27, 35, 63], we derive an application of Theorem 1.”
• Existence of positive solutions to some nonlinear equations on locally finite graphs (2016, unknown): “Keywords variational method, mountain-pass theorem, semi-linear equation on graphs MSC(2010) 34B45, 35A15, 58E30 Citation: Grigor’yan A, Lin Y, Yang Y Y. Existence of positive solutions to some nonlinear equations on locally finite graphs.”
• Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space (2011, background): “Similar problems for biLaplace equation in R4 was considered by the author in [37].”