TITLE

# A new approximation of relaxed energies for harmonic maps and the Faddeev model

AUTHOR(S)
Giaquinta, Mariano; Hong, Min-Chun; Yin, Hao
PUB. DATE
May 2011
SOURCE
Calculus of Variations & Partial Differential Equations;May2011, Vol. 41 Issue 1/2, p45
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We propose a new approximation for the relaxed energy E of the Dirichlet energy and prove that the minimizers of the approximating functionals converge to a minimizer u of the relaxed energy, and that u is partially regular without using the concept of Cartesian currents. We also use the same approximation method to study the variational problem of the relaxed energy for the Faddeev model and prove the existence of minimizers for the relaxed energy $${\tilde{E}_F}$$ in the class of maps with Hopf degree Â±1.
ACCESSION #
59439126

## Related Articles

• Iterative Schemes for a Class of Mixed Trifunction Variational Inequalities. Noor, Muhammad Aslam; Noor, Khalida Inayat; Al-Said, Eisa // Journal of Applied Mathematics;2012, p1

We use the auxiliary principle technique to suggest and analyze some iterativemethods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. The mixed trifunction variational inequality includes the trifunction variational inequalities...

• Statistical convergence and approximation theorems for functions of two variables. Mohiuddine, S. A.; Alotaibi, Abdullah // Journal of Computational Analysis & Applications;Feb2013, Vol. 15 Issue 2, p218

In this work, we use the notion of (Î», Î¼)-statistical convergence to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, xÂ² + yÂ². Furthermore, we define a new type of summability method via (Î», Î¼)-statistical...

• A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations. Yanli Zhou; Yonghong Wu; Xiangyu Ge; Wiwatanapataphee, B. // Abstract & Applied Analysis;2013, p1

Stochastic delay differential equations with jumps have a wide range of applications, particularly, inmathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we...

• Approximation by Certain Linear Positive Operators of Two Variables. Kürşat Gazanfer, Afşin; Büyükyazıcı, Ebrahim // Abstract & Applied Analysis;2014, p1

We introduce positive linear operators which are combined with the Chlodowsky and SzÃ¡sz type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by...

• ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM. Lie-heng Wang // Journal of Computational Mathematics;Jul2003, Vol. 21 Issue 4, p481

This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].

• Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function. Echebest, Nélida; Sánchez, María; Schuverdt, María // Journal of Optimization Theory & Applications;Jan2016, Vol. 168 Issue 1, p92

In the present research, an Augmented Lagrangian method with the use of the exponential penalty function for solving inequality constraints problems is considered. Global convergence is proved using the constant positive generator constraint qualification when the subproblem is solved in an...

• On Complete Convergence for Weighted Sums of p*-Mixing Random Variables. Aiting Shen; Xinghui Wang; Huayan Zhu // Abstract & Applied Analysis;2013, p1

We prove the strong law of large numbers for weighted sums ... which generalizes and improves the corresponding one for independent and identically distributed randomvariables and Ï•-mixing randomvariables. In addition, we present some results on complete convergence for weighted sums of...

• A Lobatto interpolation grid over the triangle. BLYTH, M. G.; POZRIKIDIS, C. // IMA Journal of Applied Mathematics;Feb2006, Vol. 71 Issue 1, p153

A sequence of increasingly refined interpolation grids over the triangle is proposed, with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The number of interpolation nodes, N, corresponds to a complete mth-order polynomial expansion with respect to the...

• Broken Sobolev space iteration for total variation regularized minimization problems. BARTELS, SÖREN // IMA Journal of Numerical Analysis;Apr2016, Vol. 36 Issue 2, p493

We devise an improved iterative scheme for the numerical solution of total variation regularized minimization problems. The numerical method realizes a primal-dual iteration with discrete metrics that allow for large step sizes.

Share