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Results tagged with elliptic-pde
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user 147073
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
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Is $(e^{u}+1)\Delta u+u=0$ the Euler-Lagrange equation of a functional energy?
Does there exist a functional energy $I$ such that $$(e^{u}+1)\Delta u+u=0$$ is the Euler-Lagrange equation associated with the energy functional $I$?
- 39.7k
2
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The Monge- Ampère equation with a non positive right hand side
Let $\Omega$ be a domain, $u$ and $f$ are real valued functions on $\Omega$, $(u_{ij})$ is the Hessian matrix of $u$. The function $f$ may change sign: that said, do there exist solutions for the foll …
- 52.3k