1,721,010 research outputs found
Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems
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Uniform estimates and limiting arguments for nonlocal minimal surfaces
No full textWe consider nonlocal minimal surfaces obtained by a fractional type energy functional, parameterized by s∈(0,1) . We show that the s-energy approaches the perimeter as s → 1−. We also provide density properties and clean ball conditions, which are uniform as s → 1−, and optimal lower bounds obtained by a rearrangement result. Then, we show that s-minimal sets approach sets of minimal perimeter as s → 1−
Regularity properties of nonlocal minimal surfaces via limiting arguments
No full textWe prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter s when s → 1 -.As a consequence, we obtain that all the nonlocal minimal cones are flat and that all the nonlocal minimal surfaces are smooth when the dimension of the ambient space is less or equal than 7 and s is close to 1
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