Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  find a sufficient condition guaranteeing ll-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W 1,1 (Ω; R m ) with boundary datum equal to zero.  remark that this condition does not involve global convexity of the integrand and therefore it allows us to find ll-posedness properties of two classes of nonconvex problems recently studied: functionals depending only on the gradient and radially symmetric functionals.
['Silvia Villa']
I am writing a research paper on a idea Well-posedness of Nonconvex Integral Functionals
[{"from": "human", "value": "I am writing a research paper on a idea Well-posedness of Nonconvex Integral Functionals"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  find a sufficient condition guaranteeing ll-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W 1,1 (\u03a9; R m ) with boundary datum equal to zero.  remark that this condition does not involve global convexity of the integrand and therefore it allows us to find ll-posedness properties of two classes of nonconvex problems recently studied: functionals depending only on the gradient and radially symmetric functionals."}]