Regularity theory is a branch of mathematical analysis that studies the smoothness and behavior of solutions to partial differential equations (PDEs). It investigates under what conditions these solutions possess certain regularity properties, such as continuity or differentiability, often relying on the concepts of Sobolev spaces. This theory is critical in understanding how the embeddings of these spaces relate to the solvability and uniqueness of PDEs.
congrats on reading the definition of Regularity Theory. now let's actually learn it.