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C 1 , α regularity for elliptic equations with the general nonstandard growth conditions

Sungchol Kim, Dukman Ri (2024)

Mathematica Bohemica

We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on Ω . We prove the global C 1 , α regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the C 1 , α regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.

Computational approaches to some inverse problems from engineering practice

Vala, Jiří (2015)

Programs and Algorithms of Numerical Mathematics

Development of engineering structures and technologies frequently works with advanced materials, whose properties, because of their complicated microstructure, cannot be predicted from experience, unlike traditional materials. The quality of computational modelling of relevant physical processes, based mostly on the principles of classical thermomechanics, is conditioned by the reliability of constitutive relations, coming from simplified experiments. The paper demonstrates some possibilities of...

Convergence of a method for solving the magnetostatic field in nonlinear media

Jozef Kačur, Jindřich Nečas, Josef Polák, Jiří Souček (1968)

Aplikace matematiky

For solving the boundary-value problem for potential of a stationary magnetic field in two dimensions in ferromagnetics it is possible to use a linearization based on the succesive approximations. In this paper the convergence of this method is proved under some conditions.

Critical case of nonlinear Schrödinger equations with inverse-square potentials on bounded domains

Toshiyuki Suzuki (2014)

Mathematica Bohemica

Nonlinear Schrödinger equations (NLS) a with strongly singular potential a | x | - 2 on a bounded domain Ω are considered. If Ω = N and a > - ( N - 2 ) 2 / 4 , then the global existence of weak solutions is confirmed by applying the energy methods established by N. Okazawa, T. Suzuki, T. Yokota (2012). Here a = - ( N - 2 ) 2 / 4 is excluded because D ( P a ( N ) 1 / 2 ) is not equal to H 1 ( N ) , where P a ( N ) : = - Δ - ( N - 2 ) 2 / ( 4 | x | 2 ) is nonnegative and selfadjoint in L 2 ( N ) . On the other hand, if Ω is a smooth and bounded domain with 0 Ω , the Hardy-Poincaré inequality is proved in J. L. Vazquez, E. Zuazua (2000)....

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