✦ LIBER ✦

Strong continuity of the relative rearrangement maps and application to a Galerkin approach for nonlocal problems

✍ Scribed by J.M. Rakotoson

Book ID: 103925825
Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 142 KB
Volume: 8
Category: Article
ISSN: 0893-9659
DOI: 10.1016/0893-9659(95)00086-6

No coin nor oath required. For personal study only.

✦ Synopsis

We study the strong continuity of the map u ~-+ (b.u, b.u(I u > u(.)l) ). Here, b.u = -~a ,w(a) = .f{u>u.(a)} +fo-JU>u*(a)l(bl{ .... (a)}).(r) dT for a El0, means g~[, u. (respectively, (bl{u=u.(a)}).) denotes the decreasing rearrangement of u (respectively b restricted to the set {u -u.(a)}) and IEI denotes the Lebesgue measure of a set E included in a domain ft. The results are useful for solving plasmas physics equations or any nonlocal problems involving the monotone rearrangement, its inverse or its derivatives. Keywords--Relative rearrangement, Monotone rearrangement, Galerkin method. MAIN RESULTS If we want to solve the problem: find u in H~(~) (~ open bounded set of R N) satisfying -Au = g(u~.(I u > u(x)l), b.u(lu > u(x)l)) + f(x) and use a Galerkin approximation then we will be led to consider a sequence of finite dimension spaces Vm and solve: find Um C Vm, [Turn ;¢] = 0,

📜 SIMILAR VOLUMES

Strong convergence of projection methods

Strong convergence of projection methods for a countable family of nonexpansive mappings and applications to constrained convex minimization problems

✍ Naraghirad, Eskandar 📂 Article 📅 2013 🏛 Hindawi Publishing Corporation 🌐 English ⚖ 437 KB

A spline function approach to the numeri

A spline function approach to the numerical treatment of scattering and bound-state problems for nonlocal potentials

✍ H.R. Fiebig 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 710 KB

The Lippmann-Schwinger equation for the reactance operator is converted into a system of linear equations. By using spline functions the principal-value singularity of the integral kernel can be treated analytically. Throughout this work recurrence relations suitable for automatic computation are de

Uniformly closed replaced AKTT or∗AKTT c

Uniformly closed replaced AKTT or∗AKTT condition to get strong convergence theorems for a countable family of relatively quasi-nonexpansive mappings and systems of equilibrium problems

✍ Jingling Zhang,Yongfu Su,Qingqing Cheng 📂 Article 📅 2014 🏛 Springer International Publishing AG 🌐 English ⚖ 243 KB

Corrigendum to: “Strong convergence theo

Corrigendum to: “Strong convergence theorems by a new hybrid projection algorithm for fixed point problems and equilibrium problems of two relatively quasi-nonexpansive mappings” [Nonlinear Anal. Hybrid Syst. 3 (2009) 11–20]

✍ Kriengsak Wattanawitoon; Poom Kumam 📂 Article 📅 2009 🏛 Elsevier 🌐 English ⚖ 153 KB

The authors regret that the above-referenced paper contains a number of misprints. In the statement of Theorem 3.1 (Eq. (3.1)) the condition C n+1 is incorrect. In fact, the set C n+1 in Theorem 3.1 should be replaced by the following one: The proof on page 15 line 5 should be inserted with the fol

A continuation theorem on periodic solut

A continuation theorem on periodic solutions of regular nonlinear systems and its application to the exact tracking problem for the inverted spherical pendulum

✍ Luca Consolini; Mario Tosques 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 497 KB

A new approach for optimization of therm

A new approach for optimization of thermal power plant based on the exergoeconomic analysis and structural optimization method: Application to the CGAM problem

✍ Seyyed Masoud Seyyedi; Hossein Ajam; Said Farahat 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 629 KB