Year 2024

• On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces

  Publication

  • J. Maksymiuk

  - CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS - Year 2024

  In this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...

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Year 2021

• Homoclinics for singular strong force Lagrangian systems in R^N

  Publication

  • M. Izydorek
  • J. Janczewska
  • N. Waterstraat

  - CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS - Year 2021

  We will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...

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Year 2020

• The Palais–Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications

  Publication

  • L. Asselle
  • M. Starostka

  - CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS - Year 2020

  We show that the Hamiltonian action satisfies the Palais-Smale condition over a “mixed regular- ity” space of loops in cotangent bundles, namely the space of loops with regularity H^s, s ∈ (1/2, 1), in the baseand H^{1−s} in the fiber direction. As an application, we give a simplified proof of a theorem of Hofer-Viterbo on the existence of closed characteristic leaves for certain contact type hypersufaces in cotangent bundles.

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