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Anisotropic classes of homogeneous pseudodifferential symbols

Árpád Bényi, Marcin Bownik (2010)

Studia Mathematica

We define homogeneous classes of x-dependent anisotropic symbols γ , δ m ( A ) in the framework determined by an expansive dilation A, thus extending the existing theory for diagonal dilations. We revisit anisotropic analogues of Hörmander-Mikhlin multipliers introduced by Rivière [Ark. Mat. 9 (1971)] and provide direct proofs of their boundedness on Lebesgue and Hardy spaces by making use of the well-established Calderón-Zygmund theory on spaces of homogeneous type. We then show that x-dependent symbols in...

Another fixed point theorem for nonexpansive potential operators

Biagio Ricceri (2012)

Studia Mathematica

We prove the following result: Let X be a real Hilbert space and let J: X → ℝ be a C¹ functional with a nonexpansive derivative. Then, for each r > 0, the following alternative holds: either J’ has a fixed point with norm less than r, or s u p | | x | | = r J ( x ) = s u p | | u | | L ² ( [ 0 , 1 ] , X ) = r 0 1 J ( u ( t ) ) d t .

Antieigenvalue analysis for continuum mechanics, economics, and number theory

Karl Gustafson (2016)

Special Matrices

My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...

Anti-periodic solutions to a parabolic hemivariational inequality

Jong Yeoul Park, Hyun Min Kim, Sun Hye Park (2004)

Kybernetika

In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form b ( u ) , where b L loc ( R ) . Extending b to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.

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