Liouvilleliknande
Liouvilleliknande is a term used in mathematics to describe a class of results that follow the spirit of Liouville’s theorem. A Liouville-like (often called Liouville-type) result typically asserts that, under certain growth, decay, or integrability conditions, global solutions to differential equations must be trivial or assume a very restricted form. These results appear in complex analysis, partial differential equations and geometric analysis and serve to establish rigidity and nonexistence statements for solutions on the whole space.
In complex analysis, the classical Liouville theorem states that every bounded entire function on the complex
For nonlinear elliptic equations, such as Δu = f(u) in R^n, Liouville-type results assert that under certain
Methods used to prove Liouville-like results include maximum principles, Harnack inequalities, scaling and blow-up analysis, and