In this paper, we study properties of solutions of the Dominative p-Laplace equation with homogeneous Dirichlet boundary conditions in a bounded convex domain \(\Omega \). For the equation \(-{\mathcal {D}}_p u= 1\), we show that \(\sqrt{u}\) is concave, and for the eigenvalue problem \({\mathcal {D}}_p u + \lambda u=0\), we show that \(\log {u}\) is concave.

中文翻译：

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p -Laplace方程的凹幂解

在本文中，我们研究有界凸域\（\ Omega \）中具有齐次Dirichlet边界条件的占优p -Laplace方程解的性质。对于方程\（-{\ mathcal {D}} _ p u = 1 \），我们表明\（\ sqrt {u} \）是凹的，对于特征值问题\（{\ mathcal {D}} _ p u + \ lambda u = 0 \），我们证明\（\ log {u} \）是凹的。