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Concavity properties for quasilinear equations and optimality remarks
- Publication Year :
- 2023
-
Abstract
- In this paper we study quasiconcavity properties of solutions of Dirichlet problems related to modified nonlinear Schr\"odinger equations of the type $$-{\rm div}\big(a(u) \nabla u\big) + \frac{a'(u)}{2} |\nabla u|^2 = f(u) \quad \hbox{in $\Omega$},$$ where $\Omega$ is a convex bounded domain of $\mathbb{R}^N$. In particular, we search for a function $\varphi:\mathbb{R} \to \mathbb{R}$, modeled on $f\in C^1$ and $a\in C^1$, which makes $\varphi(u)$ concave. Moreover, we discuss the optimality of the conditions assumed on the source.<br />Comment: To be published on Differential and Integral Equations
- Subjects :
- Mathematics - Analysis of PDEs
26B25, 35B99, 35E10, 35J60, 35J62
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.09982
- Document Type :
- Working Paper