In this article we show the existence of weak solutions for obstacle problems for A-Dirac equations with variable growth in the setting of variable exponent spaces of Clifford-valued functions. We also obtain the existence of weak solutions to the scalar part of A-Dirac equations in space W 1,p(x) 0 (Ω,C`n).

Isometric Sobolev spaces on finite graphs are characterized. The characterization implies that the following analogue of the Banach-Stone theorem is valid: if two Sobolev spaces on 3-connected graphs, with the exponent which is not an even integer, are isometric, then the corresponding graphs are isomorphic. As a corollary it is shown that for each finite group G and each p which is not an even...

Gradient flows in the Sobolev space H1 have been shown to enjoy favorable regularity properties. We propose a generalization of prior approaches for Sobolev active contour segmentation by changing the notion of distance in the Sobolev space, which is achieved through treatment of the function and its derivative in Riemannian manifolds. The resulting generalized Riemannian Sobolev space provides...

We deal with an initial-boundary value problem for the generalized time-dependent Schrödinger equation with variable coefficients in an unbounded n–dimensional parallelepiped (n ≥ 1). To solve it, the Crank-Nicolson in time and the polylinear finite element in space method with the discrete transparent boundary conditions is considered. We present its stability properties and derive new error e...

Let 0 < a < 1 and set Φ(t) = |t|, ∀ t ∈ R. Let 1 < p < ∞ and n ≥ 1. We prove that the superposition operator u 7→ Φ(u) maps the Sobolev space W (R) into the fractional Sobolev space W (R). We also investigate the case of more general nonlinearities. Résumé. Superposition avec des puissances sousunitaires dans les espaces de Sobolev. Pour 0 < a < 1, soit Φ(t) = |t|, ∀ t ∈ R. Soient 1 < p < ∞ et ...

In this paper, we get the quantitative space-time behavior of full Boltzmann equation with soft potentials (−2<γ<0) in close to equilibrium setting, under some velocity decay assumption, but without any Sobolev regularity assumption on initial data. We find that both large time and spatial behaviors depend data exponent γ. The key step our strategy is obtain L∞ bound a suitable weighted directl...