On a fractional harmonic replacement
نویسندگان
چکیده
Given s ∈ (0, 1), we consider the problem of minimizing the Gagliardo seminorm in H with prescribed condition outside the ball and under the further constraint of attaining zero value in a given set K . We investigate how the energy changes in dependence of such set. In particular, under mild regularity conditions, we show that adding a set A to K increases the energy of at most the measure of A (this may be seen as a perturbation result for small sets A). Also, we point out a monotonicity feature of the energy with respect to the prescribed sets and the boundary conditions.
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