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Mathematics
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murcho
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Currently doing a PhD in mathematics. My main field of research is variational calculus (in particular, nonlinear elasticity) and I have also studied some nonlinear functional analysis with applications to PDEs.

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4
Connectedness of the boundary of a domain
Sep 21, 2023
question
2
How do I show the function $I:\mathbb{R}^{+}\rightarrow\mathbb{R}$ defined by $I(x)=\int_{0}^{x} \frac{dt}{\sqrt{e^{x}-e^{t}}}$ has a unique maximum?
Nov 21, 2021
question
1
All the solutions of the 2-dim PDE $-\Delta u=\lambda e^{u}$ with boundary conditions $u=0$ are like $\log \frac{8b}{(1+\lambda b r^{2})^2}$
Nov 24, 2021
question
0
Is the Gauss map $N : \partial \Omega \rightarrow \mathcal{S}^{d-1}$ an open map?
Aug 1
question
-1
If $f\in S$ and $|f|\leq M$ in the unit circle, then show that $g(z)=\frac{f(z)}{[1+\frac{e^{i\gamma}}{M}f(z)]^2}$ is univalent. [closed]
Dec 28, 2021