Poincaré-type inequalities for the homotopy operator with \(L^{\varphi }(\varOmega )\)-norms
Based on the notion of \(L^s \) averaging domains defined by \textit{S. G. Staples} [in: Proceedings of the international conference on differential and difference equations and their applications, Melbourne, FL, USA, 2005. New York: Hindawi Publishing Corporation. 1041--1048 (2006; Zbl 1129.43005)], the first author extended the space \(L^s(\Omega)\) to the Orlicz space in [Comput. Math. Appl. 47, No.~10--11, 1611--1618 (2004; Zbl 1063.30022); Proc. Am. Math. Soc. 132, No.~8, 2367--2375 (2004; Zbl 1127.35021)]. With the aid of this notion, the Poincaré inequality for the homotopy operator on the space \(L^\varphi(\Omega)\) is extended.
scientific article; zbMATH DE number 5903375