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On bounded univalent functions that omit two given values

100%

Betsakos D.

Colloquium Mathematicum

1999

tom 80

nr 2

253-258

Let a,b ∈ {z: 0<|z|<1} and let S(a,b) be the class of all univalent functions f that map the unit disk 𝔻 into 𝔻\{a,b} with f(0)=0. We study the problem of maximizing |f'(0)| among all f ∈ S(a,b). Using the method of extremal metric we show that there exists a unique extremal function which maps 𝔻 onto a simply connnected domain $D_0$ bounded by the union of the closures of the critical trajectories of a certain quadratic differential. If a<0

Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics

88%

Rencławowicz J., Zajączkowski W. M.

Applicationes Mathematicae

1998-1999

tom 25

nr 2

221-252

Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method of successive approximations.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Colloquium Mathematicum

1 Betsakos D.

1 Rencławowicz J.

1 Zajączkowski W. M.

1 1999

1 1998

Wyniki wyszukiwania

On bounded univalent functions that omit two given values

Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics