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Results tagged with ap.analysis-of-pdes
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user 143419
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
3
votes
0
answers
160
views
Green function of an elliptic operator
Let $L$ be an elliptic operator on $\Bbb C$ with
$$\DeclareMathOperator{\Img}{Im}
L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} \, dw
$$ where $K_1$ is the mod …
0
votes
0
answers
35
views
Derivate involving Bessel function of second type
Let.
$$f := (x, y) \mapsto \text{BesselK}(1, c \cdot (a - b \cdot (x + y))) \cdot \exp(c \cdot b \cdot (y - x))$$
Is there a close formula for this $$\frac{\partial^{m+n}}{\partial y^m \partial x^n} f …
- 113