We employing a minimization arguments on appropriate Nehari manifolds, we obtain ground state solutionsfor non-local elliptic system driven by the fractional a(.)-Laplacian operator, with Dirichlet boundaryconditions type.

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

For elliptic operators in divergence form with ?-periodic coefficients of an arbitrary even order 2m ? 4 we obtain ?2-order approximations resolvents the energy operator norm as ? ? 0.

Those homogeneous polynomials P are characterized for which for arbitrary lower order polynomials Q the partial differential operator (P+Q)(D) admits a continuous linear right inverse if regarded as an operator from the space of all C∞functions on R into itself. It is shown that P has this property if and only if P is of principal type and real up to a complex constant and has no elliptic factor.

In this work, we consider the Cauchy problem for u′ − Au = f with A the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of the operator of maximal regularity f 7→ Au and its adjoint on appropriate Hardy spaces which we define and study for this purpose. As a consequence we reobtain t...

In this article we provide global subelliptic estimates for the linearized inhomogeneous Boltzmann equation without angular cutoff, and show that some global gain in the spatial direction is available although the corresponding operator is not elliptic in this direction. The proof is based on a multiplier method and the so-called Wick quantization, together with a careful analysis of the symbol...

In this paper we establish commutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in upper half-space R+n+1:={(x,t)∈Rn×(0,∞)}, with uniformly complex elliptic, L∞, t-independent coefficients. By standard pull-back mechanism, these results extend corresponding of Kenig, Lin and Shen Laplacian Lipschitz domain, which have application theory homogen...