Babuška–Lax–Milgram theorem

The Babuška–Lax–Milgram theorem is a result in functional analysis and the theory of partial differential equations (PDEs), particularly concerning the solvability of boundary value problems. It is named after mathematicians Ivo Babuška, Gilbert Lax, and Alexander Milgram, who contributed to its development. The theorem provides conditions under which a linear operator associated with a boundary value problem possesses a unique solution and characterizes this solution in terms of bounded linear functionals.