Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Weak reverse Hölder inequality of weakly A-harmonic sensors and Hölder continuity of A-harmonic sensors | Wang and Bao Journal of Inequalities and Applications 2011 2011 99 http content 2011 1 99 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Weak reverse Holder inequality of weakly A-harmonic sensors and Holder continuity of A-harmonic sensors Tingting Wang and Gejun Bao Correspondence baogj@. cn Department of Mathematics Harbin Institute of Technology Harbin 150001 PR China Springer Abstract In this paper we obtain the weak reverse Holder inequality of weakly A-harmonic sensors and establish the Holder continuity of A-harmonic sensors. Mathematics Subject Classification 2010 58A10 35J60 Keywords Weak reverse Holder inequality Weakly A-harmonic sensors Holder continuity 1 Introduction In this paper we consider the A-harmonic equation d A x du 0 where mapping A Q X A l 2 3 Rn Al Rn satisfies the following assumptions for fixed 0 a b 1 A satisfies the Carathéodory measurability condition 2 for e Q and all f e A1 R A x ệ I a A x I p p-1 3 for e Q and all f e A1 R l e R A x Xệ Ấ Ấ p-2A x I Here 1 p is a fixed exponent associated with . Remark The notions and basic theory of exterior calculus used in this paper can be found in 1 and 2 we do not mention them here. Definition 2 A solution u to called A-harmonic tensor is an element of the aA P Ị cs K 1 1 oui Uiev space Wjoc 21 SUCH trtat ị A x du dộ dx 0 a for all j e W1 p Q Al - 1 with compact support. In particular we impose the growth condition A x I I p 2011 Wang and Bao licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Wang and Bao Journal of Inequalities and Applications 2011 2011 99 http content 2011 1 99 Page 2 of 10 then .
