Boundary Problem with an Area Constraint - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T20:59:10Z http://mathoverflow.net/feeds/question/118098 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118098/boundary-problem-with-an-area-constraint Boundary Problem with an Area Constraint unknown (yahoo) 2013-01-05T00:05:45Z 2013-02-16T16:22:00Z <p>Consider a boundary given by vertices (0,a), (0,0) and (1,0) (an 'L' shaped boundary).</p> <p>The problem is to find the equation that passes between the endpoints (0,a) (1,0) of minimum length that encloses a specified area A.</p> <p>A trivial case would be A=a/2 in which case the solution would be a line.</p> <p>This is one dimensional Laplace problem with two boundaries (area and verticies) but how do I try to get a series solution for A http://mathoverflow.net/questions/118098/boundary-problem-with-an-area-constraint/119333#119333 Answer by Emanuele Paolini for Boundary Problem with an Area Constraint Emanuele Paolini 2013-01-19T14:26:10Z 2013-01-19T14:26:10Z <p>The solution should be an arc of circle enclosing appropriate area.</p>