I would like to solve the 2D Laplace equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} =0$ on the positive upper half plane: $0 <x<\infty$ and $0 < y < \infty$. The domain is bounded by a curve $y=x^a,a>1, a \in \mathbb{R}$ on the left hand side. Which complex transformation can map this domain to a simple unit circle or any easily solveable domain?
2026-03-29 14:25:25.1774794325
Conformal transformation of a region bounded by a curve $y=x^a, a \in \mathbb{R}$
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