Dissertation > Excellent graduate degree dissertation topics show

On a Singular Variational Problem

Author: TanJingGang
Tutor: YangJianFu
School: Wuhan Institute of Physics and Institute of Mathematics
Course: Basic mathematics
Keywords: Hardy inequality elliptic equation concentration-compactness principle
CLC: O176
Type: Master's thesis
Year: 2003
Downloads: 16
Quote: 0
Read: Download Dissertation

Abstract


In this paper, we deal with the singular variational problems: S(a,b,λ0):=(?)∫RN(|x|-am|▽u|m0|x|-(a+1)m|u|m)dx/∫RN|x|-bp|u|pdx)m/p,as well as (?)=(?)(b,bλ1,λ2):=(?)∫RNJ(v,v)dx/(∫RN|x|-bp|u|α|u|βdx)m/p,where J(u, v)=|x|-am|▽u|m1|x|(-(a+1)m|u|m+|x|-am|▽v|m2|x|-(a+1)m|v|m,N≥m+1>2, 0≤a<N-m/m,a≤b<a+1 and p=p(a,b)=α+β=Nm/N-m+m(b-a),α,β≥1, E≡Da 1,m(RN). The aim of this paper is to show the exis-tence of minimizer for S(a, b,λ0) and (?)(a, b,λ12).

Related Dissertations

  1. Beltrami System with Two Characteristic Matrices in High-dimensional Spaces,O175
  2. Generalization of Hardy Inequality on N-dimension Spaces,O178
  3. The existence of a class of p-Laplacian equations with multiplicity,O241.82
  4. Compact Difference Scheme for Elliptic Equations with Variable Coefficients,O241.82
  5. Positive Solution to P-Laplacian Type Scalar Field Equation in R~N with Nonlinearity Asymptotic to u~(p-1) at Infinity,O175.2
  6. Finite Element Method for General Two-Dimentional Nonlinear Singular Problems,O241.82
  7. A Generalization of Concentration-Compactness Principle and Its Applications in Problems with Critical Growth,O175.2
  8. The Finite Element Methods for Fourth Order Elliptic Equations in Three Spatial Dimensions and Incompressible Fluids,O241.82
  9. Twice Means and Hardy Inequality,O178
  10. The Study on Some Problems on Positive Solutions of Elliptic Equations and Systems,O175.25
  11. Positive Entire Solutions of Singular Non-linear Harmonic Equations(Systems),O175.25
  12. On a Class of Semilinear Elliptic Equations,O175.25
  13. Symmetric Finite Volume Element Methods for Flow Problems in Porous Media,O357.3
  14. A number of issues related to surface isometric embedding,O186.1
  15. Dynamics in Neural Networks with Delays,O175
  16. Blow-up Theory and Maximum Principle for Some Nonlinear Partial Differential Equations,O175.29
  17. On Euler-Poisson Equations,O175.2
  18. Some Mechanical Methods in Soliton Theory and Differential Geometry,O186
  19. Well-Posedness and Regularity of Boundary Vaule Problem for a Class of Second Order Degenerate Elliptic Equations,O175.25
  20. Research on Invariant Sets Method and the Eigenvalues of Degenerate Elliptic Operator,O177.91

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Calculus of variations
© 2012 www.DissertationTopic.Net  Mobile