The Banach space of L^p functions whose weak derivatives up to order k lie in L^p. Essential for variational PDE: embeddings, trace, and compactness theorems.
Sobolev space W^{k,p}
Related concepts
- Lp space
- Distribution (generalised function)
- Weak solution
- Sobolev embedding theorem
- Finite element method
- Poincaré inequality
- Distributions (Schwartz)
- Dirichlet problem (Laplace equation)
- Capacity (electrostatic + Newtonian)
- Direct method (Tonelli-Weierstrass)
- Uhlenbeck compactness (1982)
- Quasi-convexity (Morrey 1948)
- Barometric formula: p(z) = p₀·exp(−z/H), H = k_B T/(m g)
- Finite element method (Courant 1943)