TITLE

Further PDE methods for weak KAM theory

AUTHOR(S)
Evans, Lawrence C.
PUB. DATE
August 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Aug2009, Vol. 35 Issue 4, p435
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We introduce and make estimates for several new approximations that in appropriate asymptotic limits yield the key PDE for weak KAM theory, namely a Hamilton�Jacobi type equation for a potential u and a coupled transport equation for a measure s. We revisit as well a singular variational approximation introduced in Evans (Calc Vari Partial Differ Equ 17:159�177, 2003) and demonstrate �approximate integrability� of certain phase space dynamics related to the Hamiltonian flow. Other examples include a pair of strongly coupled PDE suggested by the Lions�Lasry theory (Lasry and Lions in Japan J Math 2:229�260, 2007) of mean field games and a new and extremely singular elliptic equation suggested by sup-norm variational theory.
ACCESSION #
37380652

 

Related Articles

  • Structure of Polynomial-Time Approximation. Leeuwen, Erik; Leeuwen, Jan // Theory of Computing Systems;May2012, Vol. 50 Issue 4, p641 

    Approximation schemes are commonly classified as being either a polynomial-time approximation scheme (ptas) or a fully polynomial-time approximation scheme (fptas). To properly differentiate between approximation schemes for concrete problems, several subclasses have been identified:...

  • Approximate tests in unbalanced two-way random models without interaction. Güven, Bilgehan // Statistical Papers;Aug2012, Vol. 53 Issue 3, p753 

    In the presence of non-normality, we consider testing for the significance of the variance components in the unbalanced two-way random model without interaction. The approximate test is based on the F-statistic for this model. The asymptotic distribution of the F-statistic is derived as the...

  • Simultaneous confidence intervals on partial means of classes in the two-stage stratified sampling. Cozzucoli, Paolo // Statistical Papers;Sep2010, Vol. 51 Issue 3, p673 

    Let’s consider a finite population of P units, each of them assumes a specific amount of the quantitative variable X. Moreover we assume that the range of values of X is subdivided into k classes and the sampling data come out from a two stage stratified sampling. The main purpose of the...

  • On confidence bands for multivariate nonparametric regression. Proksch, Katharina // Annals of the Institute of Statistical Mathematics;Feb2016, Vol. 68 Issue 1, p209 

    In a multivariate nonparametric regression problem with fixed, deterministic design asymptotic, uniform confidence bands for the regression function are constructed. The construction of the bands is based on the asymptotic distribution of the maximal deviation between a suitable nonparametric...

  • Estimates of deviations from exact solutions of variational inequalities based upon Payne�Weinberger inequality. Repin, S. // Journal of Mathematical Sciences;Mar2009, Vol. 157 Issue 6, p874 

    A new method for obtaining computable estimates for the difference between exact solutions of elliptic variational inequalities and arbitrary functions in the respective energy space is suggested. The estimates are obtained by transforming the corresponding variational inequality without the use...

  • Method of asymptotic integration for solutions of Lorenz-type systems. Leonov, G. // Doklady Mathematics;May2015, Vol. 91 Issue 3, p352 

    The article discusses the use of asymptotic integration on Tigan and Lorenz-type systems solution. Topics discussed include the homoclinic trajectories for the systems, the Rabinovich and Glukhovskoi-Dolzhan-skii systems, and analysis of separatrices. Also mentioned factors that should be...

  • RANDOMIZED LONGEST-QUEUE-FIRST SCHEDULING FOR LARGE-SCALE BUFFERED SYSTEMS. DIEKER, A. B.; SUK, T. // Advances in Applied Probability;Dec2015, Vol. 47 Issue 4, p1015 

    We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling (LQF) algorithm by establishing new mean-held limit theorems as the number of buffers n → ∞. We achieve this by allowing the number of sampled buffers d = d(n) to...

  • Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality. Dongyang Shi; Hongbo Guan; Xiaofei Guan // Journal of Applied Mathematics;2012, p1 

    This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconforming EQrot FE schemes under a reasonable regularity of the exact solution u ∊ H5/2(O), which...

  • Multifractal Analysis of Asymptotically Additive Sequences. Barreira, Luis; Cao, Yongluo; Wang, Juan // Journal of Statistical Physics;Dec2013, Vol. 153 Issue 5, p888 

    For saturated maps, we effect a complete multifractal analysis of the dimension spectra obtained from asymptotically additive sequences of continuous functions. This includes, for example, the class of maps with the specification property. We consider also the more general cases of ratios of...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics