Sobolev Space

A Banach (or Hilbert) space of equivalence classes of functions on a domain whose weak derivatives up to a specified order belong to an Lp space; commonly denoted W^{k,p} or H^{k} for p=2.

A family of function spaces W^{k,p} (or H^s when p=2) that measure both p‑integrability and weak differentiability up to integer order k (or fractional order s) by equipping functions with norms combining L^p norms of the function and its weak derivatives.

A Banach or Hilbert space of functions or distributions on a domain endowed with a norm that measures integrability and the size of weak derivatives up to a specified order; typically denoted W^{k,p} or H^s and fundamental to variational formulations and PDE theory.