Haar inequality in hereditary setting and applications
Hamilton-Jacobi functional differential equations with unbounded delay
The Cauchy problem for nonlinear functional differential equations on the Haar pyramid is considered. The phase space for generalized solutions is constructed. An existence theorem is proved by using the method of successive approximations. The theory of characteristics and integral inequalities are used. Examples of phase spaces are given.
Hardy-Poincaré type inequalities derived from p-harmonic problems
We apply general Hardy type inequalities, recently obtained by the author. As a consequence we obtain a family of Hardy-Poincaré inequalities with certain constants, contributing to the question about precise constants in such inequalities posed in [3]. We confirm optimality of some constants obtained in [3] and [8]. Furthermore, we give constants for generalized inequalities with the proof of their optimality.
Harmonic mappings with partially free boundary.
Harmonic maps which solve a free-boundary problem.
Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions.
Hearing the shape of a general convex domain: an extension to higher dimensions
Hearing the shape of membranes: Further results.
Heat Conduction Dominated by Electromagnetic Radiation
Hierarchical grid coarsening for the solution of the Poisson equation in free space.
High-order fractional partial differential equation transform for molecular surface construction
Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional...
Hitting properties of a random string.
Hölder continuity for sub-elliptic systems under the sub-quadratic controllable growth in Carnot groups
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth...
Holomorphic solution for classes of forced Korteweg-de Vries equations of fractional order
Homogénéisation des équations de la diffusion stationnaire dans les domaines cylindriques aplatis
Homogenization and ergodic theory
Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit
In this paper, we consider two-scale limits obtained with increasing homogenization periods, each period being an entire multiple of the previous one. We establish that, up to a measure preserving rearrangement, these two-scale limits form a martingale which is bounded: the rearranged two-scale limits themselves converge both strongly in L2 and almost everywhere when the period tends to +∞. This limit, called the Two-Scale Shuffle limit, contains all the information present in all the two-scale...
Homogenization of a carcinogenesis model with different scalings with the homogenization parameter
In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell....
Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications