Regularity and Bernstein-type results for nonlocal minimal surfaces
Regularity and Bernstein-type results for nonlocal minimal surfaces
Abstract We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi [6] stating that the validity of Bernstein’s theorem in dimension <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {n+1} is a consequence of the …