Boundary estimates and the dominance of differential operators are important concepts in mathematics that are widely used in the study of partial differential equations and boundary value problems. These concepts provide valuable insights into the behavior of solutions near boundaries and the relative importance of different terms in a differential equation.
Boundary estimates refer to quantitative estimates of the behavior of solutions to partial differential equations near the boundary of a domain. These estimates provide information about the regularity and decay properties of solutions and are crucial for understanding the well-posedness of boundary value problems. By establishing boundary estimates, mathematicians can determine the optimal regularity and decay rates of solutions near the boundary.
