# Symmetric boundary values for the Dirichlet problem for harmonic maps from the disc into the 2-sphere

## Related Articles

- The behavior of the free boundary near the fixed boundary for a minimization problem. Karakhanyan, A.; Kenig, C.; Shahgholian, H. // Calculus of Variations & Partial Differential Equations;Jan2007, Vol. 28 Issue 1, p15
We show that the free boundary âˆ‚{ u > 0}, arising from the minimizer(s) u, of the functional approaches the (smooth) fixed boundary âˆ‚Î© tangentially, at points where the Dirichlet data vanishes along with its gradient.

- On a resonant-superlinear elliptic problem. Cuesta, Mabel; de Figueiredo, Djairo G.; Srikanth, P.N. // Calculus of Variations & Partial Differential Equations;Jul2003, Vol. 17 Issue 3, p221
We start by discussing the solvability of the following superlinear problem ... where 1 < p < ... , O ? RN is a smooth bounded domain and f satisfies a one-sided Landesman-Lazer condition. We also consider systems of semilinear elliptic equations with nonlinearities of the above form, so...

- The effect of concentrating potentials in some singularly perturbed problems. Cerami, Giovanna; Passaseo, Donato // Calculus of Variations & Partial Differential Equations;Jul2003, Vol. 17 Issue 3, p257
The equation -eï¿½ ?u + ae(x)u = f(u) with boundary Dirichlet zero data is considered in a bounded domain O ? IRN . Under the assumption that aepsilon(x) = ainfinity > 0 concentrates, as e ? 0, round a manifold M ?. O and that f is a superlinear function, satisfying suitable growth...

- Dirichlet problem with indefinite nonlinearities. Kung-Ching Chang; Mei-Yue Jiang // Calculus of Variations & Partial Differential Equations;Jul2004, Vol. 20 Issue 3, p257
We consider the following nonlinear elliptic equation -?u - ?u = h_(x)g1(u) + h+(x)g2(u) in a bounded domain O with the Dirichlet boundary condition, h_ = 0 and h+ = 0, g1(u)u and g2(u)u are positive for |u| >> 1. Some existence results are given for superlinear g1 and g2 via the Morse theory.

- The Brezis-Nirenberg type problem involving the square root of the Laplacian. Tan, Jinggang // Calculus of Variations & Partial Differential Equations;Sep2011, Vol. 42 Issue 1/2, p21
We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

- THE SECOND ORDER ESTIMATE FOR THE SOLUTION TO A SINGULAR ELLIPTIC BOUNDARY VALUE PROBLEM. Ling Mi; Bin Liu // Applicable Analysis & Discrete Mathematics;2012, Vol. 6 Issue 2, p194
We study the second order estimate for the unique solution near the boundary to the singular Dirichlet problem -Î”u = b(x)g(u), u > 0, x âˆˆ Î©, uâˆ£âˆ‚Î© = 0, where Î© is a bounded domain with smooth boundary in â„N, g âˆˆ CÂ¹((0,âˆž), (0,âˆž)), g is...

- EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR KIRCHHOFF TYPE PROBLEM WITH CRITICAL EXPONENT. QI-LIN XIE; XING-PING WU; CHUN-LEI TANG // Communications on Pure & Applied Analysis;Nov2013, Vol. 12 Issue 6, p2773
In the present paper, the existence and multiplicity of solutions for Kirchhoff type problem involving critical exponent with Dirichlet boundary value conditions are obtained via the variational method.

- A remark on the dimension of the attractor for the Dirichlet problem of the complex Ginzburgâ€“Landau equation. Karachalios, Nikos. I. // Journal of Mathematical Physics;Aug2009, Vol. 50 Issue 8, p082701
Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proven by Melas [Proc. Am. Math. Soc. 131, 631 (2003)], we remark on a modified estimate of the dimension of the global attractor associated with the complex Ginzburgâ€“Landau (CGL) equation...

- AN APPLICATION OF THE LYAPUNOV-SCHMIDT METHOD TO SEMILINEAR ELLIPTIC PROBLEMS. Quố C Anh Ngô // Electronic Journal of Differential Equations;2005, Vol. 2005, p1
In this paper we consider the existence of nonzero solutions for the undecoupling elliptic system -Î”u = Î»u + Î´v + f(u, v), -Î”v = Î¸u + Î³v + g(u, v), on a bounded domain of â„n, with zero Dirichlet boundary conditions. We use the Lyapunov-Schmidt method and the fixed-point...