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The Existence for a Plateau Problem with Nonconvex Geometrical Constraint(PDF)


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The Existence for a Plateau Problem with Nonconvex Geometrical Constraint
School of Sciences,NUST,Nanjing 210094
existence variat io nal inequal ity minimum no nconv ex const raint Plateau pr oblem
T he so-called Plateau pro blem w ith no nconvex geomet rical constraint s is to find out H -surfaces w ith prescribed mean curvatur e, w hich is in a nonconvex g eomet rical set and sat isfies Plateau co ndit ions, that is, conformal co nditions. T his paper pr oved the existence of bounded solut ions for this kind Plateau problem by so lving a local minimizing pr oblem w ith nonco nvex co nst raint via the calculus of variat ion, equat ion w ith measures and prior est imates. T he solut ions obtained sat isfy a system of variat ional inequalit ies.


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