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How can I integrate this?
Let $\Omega\subset\mathbb{R}^N$ be a bounded domain and $\phi_1,v,\phi\in W_0^{1,p}(\Omega)$ with $p\in (1,\infty)$. How can I evaluate the integral: $$\int_0^1F(s)ds$$ where ...
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variation of a final state due to changes in period (where the period is a parameter)
I have a simple ordinary differential equation
$\frac{dx}{dt}=f(x,t,p,T)$
$x(0) = x_0$, $x(T) = x_T$
where $p$ and $T$ are constant parameters. How do I compute $\frac{dx_T}{dT}$ ? Thanks!
NOTE: I ...
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1answer
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Separation of variables and substituion; first integral from the Euler-Differential Equation for the minimal surface problem
Let $P_1=(a,y_a),P_2=(b,y_b), y\in C^1 (a,b), y_a>0,y_b>0$
And the area integral: $\int^b_a y(x) \sqrt{1+y'(x)}dx$
From the Euler differential-equation we obtain:
$$y'=1/\alpha ...
