# Questions tagged [elliptic-equations]

For questions about elliptic partial differential equations. If your question is specific to the Laplace equation, see (harmonic-functions).

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### Reduction to Fixed point theorem in PDE

Let $Q$ be an operator of the form: $$Qu:=a^{ij}D_{ij}u +b$$ where $a^{ij}$ and $b$ are functons of $(x,u,Du)$ and $u$ is a function of $x$. To reduce the existence of the solution $u$ to the fixed ...
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### Moser Iteration for Laplacian with Hardy potential

I am reading the following proof of Cao-Yan's 2010 CVPDE Paper. It's a property for solutions of Laplace equation with Hardy potential $|x|^{-2}.$ The space dimension $N \geq 3.$ Their proof is in the ...
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### Maximum Principle for Minimal Surface Equation with Dirichlet Boundary Condition

I'm an undergraduate student and I'm currently reading a classical paper for my final project for the course differential geometry on the Bernstein problem of minimal surfaces, namely, the paper: ...
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### solving nonlinear second order differential equation

I was stuck in solving the following nonlinear second order differential equation $$y''=\dfrac{1}{y}.$$ I try to use the Laplace transform to solve it but not work especially when dealing with the ...
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### Physical Interpretation of degenerate Laplacian

Consider the equation $$-\frac{\partial^2u}{\partial x^2}=-\text{div}\left(\begin{pmatrix}1&0\\0&0\end{pmatrix}\nabla\right)=0\mbox{ in }\mathbb{R}^2.$$ Solving the equation, we can conclude ...
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