Elliptic & Parabolic EquationsWorld Scientific, 2006 - 408 páginas This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them. |
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Elliptic & Parabolic Equations Zhuoqun Wu,Jingxue Yin,Chunpeng Wang No hay ninguna vista previa disponible - 2006 |
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admits a unique Assume boundary value condition bounded domain boundedness C(QT Cauchy's inequality Chapter choose conclusion converges Corollary cut-off function Denote derive Dirichlet problem dxdt elliptic equations exists a constant Harnack's inequality heat equation Hence Hölder continuous Hölder's estimate Hölder's inequality implies initial-boundary value problem integrating interior estimate Laplace's equation maximum principle nondecreasing norm obtain ordered supersolution parabolic equations Poincaré's inequality Poisson's equation positive constant depending proof of Theorem Proposition prove quasilinear quasimonotone Remark satisfies Schauder's estimates sequence smooth Sobolev spaces solution of equation solution of problem space strong solution supersolution and subsolution supu u₁ weak derivatives weak solution weak subsolution Βρ Δω θα θφ ΘΩ ΧΕΩ Ω Ω ди є драт