[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12941/jksiam.2014.18.279

CERTAIN WEIGHTED MEAN INEQUALITY

Kim, Namkwon (DEPARTMENT OF MATHEMATICS, CHOSUN UNIVERSITY)

Publication Information

Journal of the Korean Society for Industrial and Applied Mathematics / v.18, no.3, 2014 , pp. 279-282 More about this Journal

Abstract

In this paper, we report a new sharp inequality of interpolation type in $\mathbb{R}^n$ . This inequality is for controlling weighted average of a function via $L^n$ norm of the gradient of a function together with its' certain exponential norm.

Keywords

weighted mean inequality; interpolation inequality;

Citations & Related Records

Reference

1	G. Talenti, Best constant in Sobolev inequality, Annali di Mat. pura ed Applicata 110(1976), 353-372. DOI
2	S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math. 12(1959), 623-727. DOI
3	L. C. Evans and R. F. Gariepy, "Measure theory and fine properties of functions", CRC press, Florida, FL, 1992.
4	L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 13(1959), 115-162.
5	N.S. Trudinger, On imbeddings into Orlicz Sobolev spaces and some applications, J. Math. Mech. 17(1967), 473-483.
6	R. Wang, Chern-Simons vortices, Comm. Math. Phys. 137(1991), 587-597. DOI