Laplace operator

The Laplace operator is a mathematical tool used to analyze how a quantity, like temperature or pressure, varies across space. It measures the difference between the value at a specific point and the average of its surroundings. If the Laplacian is positive, the point is cooler or less concentrated than its neighbors; if negative, warmer or more concentrated. It helps identify regions where a process is spreading out, concentrating, or remaining balanced. Widely used in physics, engineering, and mathematics, it provides insight into how things diffuse or stabilize across a space.