Abstract. We study the convergence of the upwind Finite Volume scheme applied to the linear advection equation with a Lipschitz divergence-free speed in Rd . We prove a h1/2−ε-error estimate in the L∞(Rd × [0, T ])-norm for Lipschitz initial data. The expected optimal result is a h1/2-error estimate. In a second part, we also prove a h1/2-error estimate in the L(0, T ; L2(Rd))-norm for initial ...

We consider the classical inverse mapping theorem of Nash and Moser from angle some recent development by Ekeland authors. Geometrisation tame estimates coupled with certain ideas coming variational analysis when applied to a directionally differentiable produces very general surjectivity result and, if injectivity can be ensured, expected Lipschitz-like continuity inverse. also present brief a...

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved an estimate of constant computed. The main contribution work establishment equivalence relationship between graph convergence sequence strongly their mappings, respectively, to given by using no...

We study the extent to which the Hausdorff dimension of a compact subset of an infinite-dimensional Banach space is affected by a typical mapping into a finite-dimensional space. It is possible that the dimension drops under all such mappings, but the amount by which it typically drops is controlled by the ‘thickness exponent’ of the set, which was defined in [13]. More precisely, let X be a co...

In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without prior knowledge constant mapping. Finally, some numerical examples provided to illustrate efficiency advantag...

Let M and N be doubly connected Riemann surfaces with $${\mathscr {C}}^{1,\alpha }$$ boundaries nonvanishing conformal metrics $$\sigma $$ $$\wp respectively, assume that is a smooth metric bounded Gauss curvature $${\mathcal {K}}$$ finite area. Assume {H}}^\wp (M, N)$$ the class of all {W}}^{1,2}$$ homeomorphisms between {E}}^\wp : {\mathcal N)\rightarrow {\mathbf {R}}$$ Dirichlet-energy funct...

‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded‎.