One-dimensional symmetry of solutions to non-cooperative elliptic systems. (February 2023) - Le, Phuong
Abstract: We prove the monotonicity and one-dimensional symmetry of solutions to non-cooperative elliptic systems in R N with uniform limits under mild assumptions on the nonlinearities. These problems arise in the study of domain walls and interface layers of two-component Bose–Einstein condensates in the segregation regime. We also derive analogous results for systems in half-spaces and strips. We introduce a variant of the sliding method for non-cooperative elliptic systems to prove our results.