Interior Regularity Results

This lecture covers interior regularity results in the context of mathematical analysis, focusing on weak solutions and unique weak selection. The instructor explains the concept of test functions, proof techniques, and the properties of cut-off functions. The lecture also delves into the application of these results in function spaces and the regularity of solutions. Additional topics include the uniqueness of weak solutions and the extension of functions to zero. The presentation concludes with a discussion on the boundary conditions and the implications of these results.