Applications to differential equations (intro)
General · Mathematics
Study notes
Q: How does Lax-Milgram solve -u'' = f, u(0) = u(1) = 0? Weak form: ∫u'v' = ∫fv for all v ∈ H₀¹. Bilinear a(u,v) = ∫u'v': coercive (Poincaré!)! Lax-Milgram: unique weak u ∈ H₀¹! Regularity: u'' = -f: classical! (Functional analysis solves PDEs!)