# Tagged Questions

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### Is this right way to prove Riemann mapping theorem?

We can solve laplace equation $\Delta u=0$ with Dirichlet boundary condition $u(x,y)=f\in C(\partial D)$ for the unit disk $D$ $\subset$ $R^2$ . If $f$ is a continuous function on the boundary ...
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### What is a 'general proper solution' of a partial differential equation?

I would like to know what a 'general proper solution' of a partial differential equation is. The term came reading the abstract of the paper 'Quasiregular mapping by branched circle packing', but I ...
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### Why do level curves of a function and its harmonic conjugate intersect each other orthogonally?

So I've had this assignment in which I had to proof that two level curves of a function and one of its harmonic conjugates intersect each other orthogonally. The proof itself wasn't that difficult, ...
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### Fourier series for $e^x$

I'm trying to teach myself partial differential equations from Strauss' book. I have run into a very bizarre problem - I cannot figure out what is the Fourier series of $e^x$! And not even Google has ...
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### Elliptic Operators and Continuity

I am reading a book on Hodge theory (Ref: http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/hodge-smf.pdf) or for english ...
Suppose $u$ is a complex-valued wave function $u(x,y,z,t)$. Also, suppose you have the integral $\int(u\overline{u}_{t}+u_{t}\overline{u})dx$. I need to get ...