106 research outputs found
The Stokes and Poisson problem in variable exponent spaces
We study the Stokes and Poisson problem in the context of variable exponent
spaces. We prove the existence of strong and weak solutions for bounded domains
with C^{1,1} boundary with inhomogenous boundary values. The result is based on
generalizations of the classical theories of Calderon-Zygmund and
Agmon-Douglis-Nirenberg to variable exponent spaces.Comment: 20 pages, 1 figur
Smoluchowski-Kramers approximation in the case of variable friction
We consider the small mass asymptotics (Smoluchowski-Kramers approximation)
for the Langevin equation with a variable friction coefficient. The limit of
the solution in the classical sense does not exist in this case. We study a
modification of the Smoluchowski-Kramers approximation. Some applications of
the Smoluchowski-Kramers approximation to problems with fast oscillating or
discontinuous coefficients are considered.Comment: already publishe
A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide
We will study the spectral problem related to the Laplace operator in a
singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with
contains periodic arrangement of inclusions. On the boundary of the waveguide
we consider both Neumann and Dirichlet conditions. We will prove that provided
the diameter of the inclusion is small enough in the spectrum of Laplacian
opens spectral gaps, i.e. frequencies that does not propagate through the
waveguide. The existence of the band gaps will verified using the asymptotic
analysis of elliptic operators.Comment: 26 pages, 6 figure
Interval oscillation criteria for second-order nonlinear forced differential equations involving variable exponent
Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator
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