Regularity Results for Solutions of a Class of Hamilton-Jacobi Equations View Full Text


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Article Info

DATE

1997-12

AUTHORS

Piermarco Cannarsa, Andrea Mennucci, Carlo Sinestrari

ABSTRACT

The regularity of the gradient of viscosity solutions of first‐order Hamilton‐Jacobi equations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*} \begin{array}{rll} \partial_t u(t,x) + H( t, x, D_x u(t,x))=0,&\quad & t\in\real_+,\es x \in \real^n\,, \\[3pt] u(0,x) = \uzero (x), &\quad & x \in \real^n\,, \end{array} \end{eqnarray*}\end{document} is studied under a strict convexity assumption on H(t,x,⋅). Estimates on the discontinuity set of Du are derived. Such estimates imply that solutions of the above problem are smooth in the complement of a closed ℋn‐rectifiable set. In particular, it follows that Du belongs to the classSBV, i.e., D2u$ is a measure with no Cantor part. More... »

PAGES

197-223

References to SciGraph publications

  • 1992-12. On the singularities of convex functions in MANUSCRIPTA MATHEMATICA
  • 1996. Geometric Measure Theory in NONE
  • 1989-10. Variational problems in SBV and image segmentation in ACTA APPLICANDAE MATHEMATICAE
  • 1995. Generalized Solutions of First Order PDEs, The Dynamical Optimization Perspective in NONE
  • 1990-12. Existence theory for a new class of variational problems in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s002050050064

    DOI

    http://dx.doi.org/10.1007/s002050050064

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1010297606


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