# Solution to the boundary blowup problem for k-curvature equation

## Related Articles

- Decay and Continuity of the Boltzmann Equation in Bounded Domains. Yan Guo // Archive for Rational Mechanics & Analysis;Sep2010, Vol. 197 Issue 3, p713
Boundaries occur naturally in kinetic equations, and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: in-flow,...

- THE FLOATING BODY PROBLEM. A. STANCU // Bulletin of the London Mathematical Society;Oct2006, Vol. 38 Issue 5, p839
Let $K$ be a convex body with boundary of class ${\mathcal{C}}^{\geq 4}$. We prove that, for a sufficiently small $\delta$, the floating body $K_{\delta}$ is homothetic to $K$ if and only if $K$ is an ellipsoid. The proof relies on properties of the affine curvature flow.

- Method of Factorizing a Solution to Some Boundary-Value Problems. Babeshko, V. A.; Babeshko, O. M. // Doklady Physics;Mar2003, Vol. 48 Issue 3, p134
Analyzes the three-dimensional boundary-value problems for partial differential equation in bounded convex regions. Merits and demerits of the method.

- The mathematics of eigenvalue optimization. Lewis, A.S. // Mathematical Programming;Jul2003, Vol. 97 Issue 1/2, p155
Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich blend of classical mathematical techniques and...

- Projection operator technique for imposing the boundary conditions on a trial wave function. Brownstein, K. R. // Journal of Mathematical Physics;Sep93, Vol. 34 Issue 9, p4138
A projection operator technique is developed for using N linear basis functions which do not satisfy the boundary conditions. If the boundary conditions at M locations on the boundary are invoked via M constraint equations, the method leads to an N-by-N determinantal equation which is of the...

- On hearing the shape of a bounded domain with Robin boundary conditions. Zayed, EME // IMA Journal of Applied Mathematics;Feb2000, Vol. 64 Issue 1
Focuses on the Robin boundary problem, where omega is a general, multiply connected, bounded domain. Eigenvalues for the boundary problem; Applications of a ideal gas enclosed in the multiply connected bounded container with Neumann or Robin boundary conditions.

- Properties of spatial structures for reaction-nonlinear diffusion equations subject to Dirichlet conditions. Razzhevaikin, V. // Computational Mathematics & Mathematical Physics;Oct2011, Vol. 51 Issue 10, p1729
For reaction-nonlinear diffusion equations subject to Dirichlet homogeneous boundary value conditions, the properties of alternation of stable and unstable time-independent unimodal solutions are investigated. For the case of constant diffusion, formulas for the functions determining the type of...

- CONVEXITY OF THE FREE BOUNDARY FOR AN EXTERIOR FREE BOUNDARY PROBLEM INVOLVING THE PERIMETER. MIKAYELYAN, HAYK; SHAHGHOLIAN, HENRIK // Communications on Pure & Applied Analysis;May2013, Vol. 12 Issue 3, p1431
We prove that if the given compact set K is convex then a minimizer of the functional I(v) = âˆ«BR |âˆ‡v|pdx + Per({v > 0}), 1 < p < âˆž, over the set {v âˆˆ W01,p (BR)| v â‰¡ 1 on K âŠ‚ B R} has a convex support, and as a result all its level sets are convex as well. We...

- SOLUTION CURVES OF 2m-TH ORDER BOUNDARY-VALUE PROBLEMS. Rynne, Bryan P. // Electronic Journal of Differential Equations;2004, Vol. 2004, p1
We consider a boundary-value problem of the form Lu = Î»f(u), where L is a 2m-th order disconjugate ordinary differential operator (m â‰¥ 2 is an integer), Î» âˆˆ [0,âˆž), and the function f : R â†’ R is C2 and satisfies f(Îž) > 0, Îž âˆˆ R. Under various convexity or...