We discuss an innnite-dimensional version of Pontrya-gin's maximum principle as a uniied variational method in many familiar classes of analytic functions, and its interrelation with classical variational methods in geometric function theory.

We study the strong maximum principle for the heat equation associated with the Dirichlet form on an infinite network. We prove that the strong maximum principle is equivalent to the underlying graph being connected after deletion of the nodes with infinite degree. Using this result, we prove that the multiplicity of the eigenvalue 0 of a generalization of the Laplace matrix equals the number o...

The concept of uncertain entropy is used to provide a quantitative measurement of the uncertainty associated with uncertain variables. After introducing the definition, this paper gives some examples of entropy of uncertain variables. Furthermore this paper proposes the maximum entropy principle for uncertain variables, that is, out of all the uncertainty distributions satisfying given constrai...

We study, in this work, the maximum principle for the Beltrami color flow and the stability of the flow’s numerical approximation by finite difference schemes. We discuss, in the continuous case, the theoretical properties of this system and prove the maximum principle in the strong and the weak formulations. In the discrete case, all the second order explicit schemes, that are currently used, ...

In this paper, the authors study an optimal control problem for quasilinear elliptic PDEs with pointwise state constraints. Weak and strong optimality conditions of Pontryagin maximum principle type are derived. In proving these results, we penalized the state constraints and respectively use the Ekeland variational principle and an exact penalization method. In this paper, our aim is to prove ...

Some generalizations of the maximum principle for harmonic functions are discussed. §

We study, in this work, the maximum principle for the Beltrami color flow and the stability of the flow’s numerical approximation by finite difference schemes. We discuss, in the continuous case, the theoretical properties of this system and prove the maximum principle in the strong and the weak formulations. In the discrete case, all the second order explicit schemes, that are currently used, ...

In this paper we investigate optimal control problems governed by variational inequalities. We present a method for deriving optimality conditions in the form of Pontryagin's principle. The main tools used are the Ekeland's variational principle combined with penalization and spike variation techniques. 1. Introduction. The purpose of this paper is to present a method for deriving a Pontryagin ...

Various spectral Chebyshev approximations of a model boundary layer problem for both a Helmholtz and an advection-diffusion operator are considered. It is assumed that simultaneously the boundary layer width tends to zero and the resolution power of the numerical method tends to infinity. The behavior of the spectral solutions in the frequency space and in the physical space is investigated. Er...

This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle—such as the separating hyperplanes, costate, necessary condition, and normal/abnormal minimizers—have natural contactgeometric interpretations. We then exploit the contact-geometric formulation to give a simple derivation of the transversality cond...