On First and Second Order Planar Elliptic Equations with Degeneracies - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On First and Second Order Planar Elliptic Equations with Degeneracies write by Abdelhamid Meziani. This book was released on 2012. On First and Second Order Planar Elliptic Equations with Degeneracies available in PDF, EPUB and Kindle. This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.
On First and Second Order Planar Elliptic Equations with Degeneracies
On First and Second Order Planar Elliptic Equations with Degeneracies - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On First and Second Order Planar Elliptic Equations with Degeneracies write by Abdelhamid Meziani. This book was released on 2011. On First and Second Order Planar Elliptic Equations with Degeneracies available in PDF, EPUB and Kindle. This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.
The Kohn-Sham Equation for Deformed Crystals
The Kohn-Sham Equation for Deformed Crystals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Kohn-Sham Equation for Deformed Crystals write by Weinan E. This book was released on 2013-01-25. The Kohn-Sham Equation for Deformed Crystals available in PDF, EPUB and Kindle. The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.
The Regularity of General Parabolic Systems with Degenerate Diffusion
The Regularity of General Parabolic Systems with Degenerate Diffusion - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Regularity of General Parabolic Systems with Degenerate Diffusion write by Verena Bögelein. This book was released on 2013-01-28. The Regularity of General Parabolic Systems with Degenerate Diffusion available in PDF, EPUB and Kindle. The aim of the paper is twofold. On one hand the authors want to present a new technique called $p$-caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classical tool to prove linearization and regularity results for vectorial problems. Here the authors develop a very far reaching version of this general principle devised to linearize general degenerate parabolic systems. The use of this result in turn allows the authors to achieve the subsequent and main aim of the paper, that is, the implementation of a partial regularity theory for parabolic systems with degenerate diffusion of the type $\partial_t u - \mathrm{div} a(Du)=0$, without necessarily assuming a quasi-diagonal structure, i.e. a structure prescribing that the gradient non-linearities depend only on the the explicit scalar quantity.
Elliptic Integrable Systems
Elliptic Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Integrable Systems write by Idrisse Khemar. This book was released on 2012. Elliptic Integrable Systems available in PDF, EPUB and Kindle. In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.
