Direct Methods in the Theory of Elliptic Equations
            
            ISBN: , SKU: , AUTHOR: Necas, Jindrich / Tronel, Gerard / Kufner, Alois, PUBLISHER: Springer, Necas's famous book Direct ong>methodsong> in ong>theong> ong>theong>ory of elliptic equations has become standard reference material on ong>theong> maong>theong>matical ong>theong>ory of linear elliptic equations and systems, and also on ong>theong> related function spaces framework. It provides a concise and self-contained introduction to ong>theong> modern ong>theong>ory of partial differential equations, ong>theong> ong>theong>ory of weak solutions and related topics. It is recommended to scientists working in ong>theong> field of partial differential equations, postgraduate and graduate students, and applied maong>theong>maticians. ong>Theong> first chapter is devoted to directs ong>methodsong>, introduction to ong>theong> Sobolev spaces, weak solution, Lax-Milgram ong>theong>orem, Galerkin metods and spectral ong>theong>ory. ong>Theong> second chapter deals with ong>theong> basic properties of Sobolev spaces (imbeddings, traces, compact imbeddings, fractional spaces).ong>Theong> third chapter contains existence and uniqueness ong>theong>orems for problems, including ong>theong> Fredholm alternative and systems of equations with variable coefficients. ong>Theong> next chapter describes regularity properties of weak solutions. Chapter 5 deals with applications of Rellich's inequality and Chapter 6 introduces ong>theong> Sobolev spaces with weights. Finally ong>theong> last chapter studies regularity of solutions and ong>theong>ir dependence on coefficients and also on irregular domains.