Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with L1 Data | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 65825 15 pages doi 2007 65825 Research Article On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with L1 Data S. Bonafede and F. Nicolosi Received 24 January 2007 Accepted 29 January 2007 Recommended by V. Lakshmikantham We establish Holder continuity of generalized solutions of the Dirichlet problem associated to a degenerate nonlinear fourth-order equation in an open bounded set D c R with L1 data on the subsets of D where the behavior of weights and of the data is regular enough. Copyright 2007 S. Bonafede and F. Nicolosi. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction A q In this paper we will deal with equations involving an operator A w2 p v p D W2q v p Q oftheform Au ỵ -1 a DaAa x v2u a 1 2 where D is a bounded open set of R n 4 2 p n 2 max 2 p n q n v and p are positive functions in D with properties precised later w2 q v p D is the Banach space of all functions u D - R with the properties lulq vlDaulq plD uự G L1 D lal 1 p 2 and zero boundary values v2u Dau l al 2 . The functions Aa satisfy growth and monotonicity conditions and in particular the following strengthened ellipticity condition for . x G D and Ỉ a a 1 2 Aa x Wa cÁ v x a q p x Ka I p 1 - g2 x a 1 2 a 1 a 2 where c2 0 g2 x G L1 D . 2 Boundary Value Problems We will assume that the right-hand sides of our equations depending on unknown function belong to L1 Q . A model representative of the given class of equations is the following - Da lal 1 q-2 2 v IdM2 Dau Wl 1 Da lal 2 p-2 2 4 D m M Dau Wl 2 -lulơ 1u f in Q where Ơ 1 and f G L1 Q . The assumed conditions and known results of the theory of monotone operators allow us to prove existence of generalized solutions .
