Banach Spaces of Locally Schlicht Functions with the Hornich Operations.
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...
We study the idea of the boundary subordination of two analytic functions. Some basic properties of the boundary subordination are discussed. Applications to classes of univalent functions referring to a boundary point are demonstrated.