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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

0 votes
1 answer
214 views

If we don't care about uniqueness, can we relax the coercivity condition in Lax-Milgram theo...

Let $(H, \langle \cdot, \cdot \rangle)$ be a real Hilbert space and $\|\cdot \|$ its induced norm. Let $a: H \times H \to \mathbb R$ be a bilinear form. We say that $a$ is coercive IFF there is $C>0$ …
4 votes
0 answers
212 views

References for derivative w.r.t. initial condition of an ODE

Let $b:\mathbb R_+ \times \mathbb R^d \to \mathbb R^d$ be measurable such that for all $n \in \mathbb N$ we have $$ \sup_{t \ge 0} |b(t, 0)| + \sup_{t \ge 0} \sup_{x \in \mathbb R^d} |\nabla^n_x b (t, …