Abstract
AbstractIn this paper, we study properties of solutions of the Dominative p-Laplace equation with homogeneous Dirichlet boundary conditions in a bounded convex domain $$\Omega $$Ω. For the equation $$-{\mathcal {D}}_p u= 1$$-Dpu=1, we show that $$\sqrt{u}$$u is concave, and for the eigenvalue problem $${\mathcal {D}}_p u + \lambda u=0$$Dpu+λu=0, we show that $$\log {u}$$logu is concave.
Funder
NTNU Norwegian University of Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference19 articles.
1. Alvarez, O., Lasry, J., Lions, P.: Convex viscosity solutions and state constraints. J. Math. Pures Appl. 76, 265–288 (1997)
2. Attouchi, A., Parviainen, M., Ruosteenoja, E.: $$C^{1,\alpha }$$ regularity for the normalized $$p$$-Poisson problem. J. Math. Pures Appl. 108(4), 553–591 (2017)
3. Brustad, K.: Superposition of $$p$$-superharmonic functions (2018) (preprint)
4. Brustad, K.: Sublinear elliptic operators (2018) (preprint)
5. Brascamp, H.J., Lieb, E.H.: On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. J. Funct. Anal. 22(4), 366–389 (1976)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献