科研之友
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摘要
We consider the optimization problem of minimizing in the class of functions with for a given function , where is the class of weakly differentiable functions with . The conditions on the function allow for a different behavior at and at . We give a rather complete description of regularity theory for a family of two-phase variational free boundary problems. For , we prove that every minimizer of is continuous. For , we obtain local Lipschitz continuity for any minimizer of . Here we also consider an asymptotic problem as . At last, we establish sharp geometric estimates for the free boundary corresponding to the minimizer of .
