A maximum principle for the Bergman space

A Maximum Principle for the Bergman Space 481

The Maximum Principle for the Bergman Space and the Möbius Pseudodistance for the Annulus

It is shown that the formula for the Möbius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle.

A maximum principle for bounded solutions of the telegraph equation in space dimension three

A maximum principle is proved for the weak solutions u ∈ L∞(R× T3) of the telegraph equation utt − xu + cut + λu = f (t, x), in space dimension three, when c > 0, λ ∈ (0, c2/4] and f ∈ L∞(R × T3) (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semili...

The Pontryagin Maximum Principle

Theorem (PontryaginMaximum Principle). Suppose a final time T and controlstate pair (û, x̂) on [τ, T ] give the minimum in the problem above; assume that û is piecewise continuous. Then there exist a vector of Lagrange multipliers (λ0, λ) ∈ R × R with λ0 ≥ 0 and a piecewise smooth function p: [τ, T ] → R n such that the function ĥ(t) def =H(t, x̂(t), p(t), û(t)) is piecewise smooth, and one has ̇̂ ...

A Maximum Principle for Combinatorial Yamabe Flow

In his proof of Andreev’s theorem, Thurston in [1] introduced a conformal geometric structure on two dimensional simplicial complexes which is an analogue of a Riemannian metric. He then used a version of curvature to prove the existence of circle-packings (see also Marden-Rodin [2] for more exposition). Techniques very similar to elliptic partial differential equation techniques were used by Y...