# A microscopic convexity theorem of level sets for solutions to elliptic equations

## Related Articles

- Maximum principle for semi-elliptic trace operators and geometric applications. Bessa, G.; Pessoa, Leandro // Bulletin of the Brazilian Mathematical Society;Jun2014, Vol. 45 Issue 2, p243
Based on ideas of L. AlÃas, D. Impera and M. Rigoli developed in [13], we present a fairly general weak/Omori-Yau maximum principle for trace operators. We apply this version of maximum principle to generalize several higher order mean curvature estimates and to give an extension of...

- Large solutions to complex Monge-AmpÃ¨re equations: Existence, uniqueness and asymptotics. Xiang, Ni; Yang, Xiaoping // Chinese Annals of Mathematics;Jul2011, Vol. 32 Issue 4, p569
The authors consider the complex Monge-AmpÃ¨re equation det $\left( {u_{i\bar j} } \right)$ = Ïˆ( z, u, âˆ‡ u) in bounded strictly pseudoconvex domains Î©, subject to the singular boundary condition u = âˆž on âˆ‚Î©. Under suitable conditions on Ïˆ, the existence, uniqueness...

- Measuring the level sets of anisotropic homogeneous functions. Aimar, Hugo; Gómez, Ivana // Positivity;Sep2011, Vol. 15 Issue 3, p401
In this note we investigate some basic properties of the level sets of functions which are homogeneous with respect to nonisotropic dilations. In particular we obtain a formula for the volume of the level sets in terms of the area on the level surfaces. We relate the results to some well known...

- Shock wave solutions of the variants of the Kadomtsev-Petviashvili equation. Triki, Houria; Sturdevant, B.J.M.; Hayat, T.; Aldossary, O.M.; Biswas, A. // Canadian Journal of Physics;Sep2011, Vol. 89 Issue 9, p979
This study obtained the shock wave or kink solutions of the variants of the Kadomtsev-Petviashvili equation with generalized evolution. There are three types of variants of this equation that were considered. The relation between the parameters and the constraint conditions will naturally fall...

- Multi-dimensional Weiss operators. Borisenok, Sergey; Erkut, M. Hakan; Polatoğlu, Yaşar; Demırer, Murat // Turkish Journal of Mathematics;2011, Vol. 35 Issue 4, p687
We present a solution of the Weiss operator family generalized for the case of â„d and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a subset of null class functions for a partial differential equation...

- Erratum to: Risk-Sensitive Control with Near Monotone Cost. Biswas, Anup; Borkar, V.; Suresh Kumar, K. // Applied Mathematics & Optimization;Nov2010, Vol. 62 Issue 3, p435
No abstract available.

- Counting smooth solutions to the equation A+B=C. Lagarias, J. C.; Soundararajan, K. // Proceedings of the London Mathematical Society;Apr2012, Vol. 104 Issue 4, p770
This paper studies integer solutions to the abc equation A+B=C in which none of A, B, C has a large prime factor. We set H(A, B, C)=max(|A|, |B|, |C|), and consider primitive solutions (g.c.d.(A, B, C)=1) having no prime factor p larger than (log H(A, B, C))Îº, for a given finite Îº. On the...

- Some solitary wave solutions of generalized Pochhammer-Chree equation via Exp-function method. Parand, Kourosh; Rad, Jamal Amani // World Academy of Science, Engineering & Technology;Jul2010, Issue 43, p423
No abstract available.

- On the local smoothness of weak solutions to the MHD system near the boundary. Vyalov, V. // Journal of Mathematical Sciences;Sep2012, Vol. 185 Issue 5, p659
We establish conditions sufficient for the local regularity of suitable weak solutions to the MHD system near the plane part of the boundary. Bibliography: 9 titles.