Sharp integral inequalities for harmonic functions

By Fengbo Hang, Xiaodong Wang, Xiaodong Yan. 2006

67 citations recorded by the source corpus.

Motivated by Carleman's proof of isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper half‐space. We also derive the regularity for nonnegative solutions of the associated integral system and some Liouville‐type theorems. © 2007 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1fe5f7561d9d679e0f1dad57ea6efae270ad61dd

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. Fengbo Hang
2. Jingbo Dou
3. Meijun Zhu
4. Paul Yang
5. David Kalaj
6. Yanyan Li
7. A. Malchiodi
8. María del Mar González

In Computational Theory and Mathematics

1. Jingbo Dou
2. Meijun Zhu
3. David Kalaj
4. Fengbo Hang
5. Paul Yang
6. Wenxiong CHEN *
7. Congming LI #

In Mathematical Physics

1. Jingbo Dou
2. Meijun Zhu
3. David Kalaj
4. Fengbo Hang
5. Paul Yang
6. Qiaohua Yang
7. Guozhen Lu
8. Yanyan Li

Citations in the corpus

• SHARP HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE (2013, methodology): “[27] F. Hang, X. Wang, X. Yan, Sharp integral inequalities for harmonic functions, Comm. Pure Appl.”
• On the integral systems related to Hardy-Littlewood-Sobolev inequality (2007, methodology): “Another motivation comes from the study of regularity issues for a similar integral system in [ 7 ].”
• On Riesz type inequalities for harmonic mappings on the unit disk (2017, background): “n Tand U, respectively, the previous inequality can be written in the form (2.14) Z U |f(z)|2 ≤ Z T |f(z)| 2 . This inequality has been proved independently by Mateljevic´ and Pavlovic´ ([13]). In [4], F. Hang, X. Wang, X. Yan have made a certain generalizations for the space. Now we prove the foll”
• Q‐Curvature on a Class of Manifolds with Dimension at Least 5 (2014, background): “4 to the classical Yamabe problem [24, 31] and the integral equation considered in [13, 14].”