A SUBLINEAR SOBOLEV INEQUALITY FOR p-SUPERHARMONIC FUNCTIONS

作者：Nguyen Cong Phuc^*

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145(1): 327-334.

DOI：10.1090/proc/13322

We establish a "sublinear" Sobolev inequality of the form
(1,1) (integral(Rn) nq/Un - q dx)(n - q/nq) <= C (integral(Rn) vertical bar Du vertical bar(q)dx)(1/q)
for all global p-superharmonic (1 < p < 2) functions u in R-n, n >= 2, with inf(Rn) u = 0 and p 1 < q < 1. The same result also holds for the class of A-superharmonic functions. More general sublinear trace inequalities, where Lebesgue measure is replaced by a general measure, are also considered.

• 出版日期2017-1