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boundary condition in VariationalBound


Is there any way to include the the boundary condition into
VariationalBound?

VariationalBound[Sqrt[1 + Derivative[1][y][x]^2], y[x], {x, 0, 1}, a +
b x, {a}, {b}]

gives

{1., {b -> 0}}

which really minimizes the functional but in the class of all linear
functions not restricting the minimization onto those which fulfil,
say, y[0]=0, y[1]=1.

Perhaps one should reformulate the problem?

The same problem does not arise when usin EulerEquations or
VariationalD.

Thank you.

J=E1nos



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