0
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1answer
150 views

Boundary Problem with an Area Constraint

Consider a boundary given by vertices (0,a), (0,0) and (1,0) (an 'L' shaped boundary). The problem is to find the equation that passes between the endpoints (0,a) (1,0) of minimum length that ...
2
votes
0answers
231 views

Monge Ampere and Calculus

[ I posted the question on Math StackExchange but didn't get any reply nor comment, so I'm trying here ] I am learning about mass transportation theory and the Monge-Ampere equation, to transport a ...
1
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2answers
237 views

Singularity at left endpoint for variational calculus problem

Hi all, first, I'd like to apologize if the term "singularity" is being misused. I have the following integral: $\int _{0}^{\pi/2} \sqrt{ r \left( x \right) ^{2} + \left( {\frac {d}{dx}} r \left( x ...
4
votes
2answers
1k views

Minimizing a function containing an integral

I am trying to optimize a function of the following form: $L = \int_{t=0}^{T}(AR-x)dt$, where A is a system parameter i.e. I am trying to find the optimum x(t) that minimizes L over all admissible ...