On the optimality of velocity averaging lemmas

Camillo de Lellis; Michael Westdickenberg

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 6, page 1075-1085
  • ISSN: 0294-1449

How to cite

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de Lellis, Camillo, and Westdickenberg, Michael. "On the optimality of velocity averaging lemmas." Annales de l'I.H.P. Analyse non linéaire 20.6 (2003): 1075-1085. <http://eudml.org/doc/78603>.

@article{deLellis2003,
author = {de Lellis, Camillo, Westdickenberg, Michael},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {kinetic equations; velocity averaging; regularity; Burgers equation; finite entropy dissipation},
language = {eng},
number = {6},
pages = {1075-1085},
publisher = {Elsevier},
title = {On the optimality of velocity averaging lemmas},
url = {http://eudml.org/doc/78603},
volume = {20},
year = {2003},
}

TY - JOUR
AU - de Lellis, Camillo
AU - Westdickenberg, Michael
TI - On the optimality of velocity averaging lemmas
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 6
SP - 1075
EP - 1085
LA - eng
KW - kinetic equations; velocity averaging; regularity; Burgers equation; finite entropy dissipation
UR - http://eudml.org/doc/78603
ER -

References

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  1. [1] Ambrosio L., De Lellis C., Mantegazza C., Line energies for gradient vector fields in the plane, Calc. Var. Partial Differential Equations9 (4) (1999) 327-355. Zbl0960.49013MR1731470
  2. [2] Aviles P., Giga Y., A mathematical problem related to the physical theory of liquid crystal configurations, Proc. Centre Math. Anal. Austral. Nat. Univ.12 (1987) 1-16. MR924423
  3. [3] De Giorgi E., Definizione ed espressione analitica del perimetro di un insieme, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat.14 (8) (1953) 390-393. Zbl0051.29403MR56066
  4. [4] C. De Lellis, Energie di linea per campi di gradienti, Ba. D. Thesis, University of Pisa, 1999. 
  5. [5] C. De Lellis, F. Otto, M. Westdickenberg, Structure of entropy solutions for multi-dimensional scalar conservation laws, Preprint n° 95/2002 at http://www.mis.mpg.de/preprints/2002. Zbl1036.35127MR1985613
  6. [6] Jabin P.-E., Perthame B., Regularity in kinetic formulations via averaging lemmas. A tribute to J.-L. Lions, ESAIM Control Optim. Calc. Var.8 (2002) 761-774. Zbl1065.35185MR1932972
  7. [7] Jin W., Kohn R.V., Singular perturbation and the energy of folds, J. Nonlinear Sci.10 (3) (2000) 355-390. Zbl0973.49009MR1752602
  8. [8] Lions P.-L., Perthame B., Tadmor E., A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc.7 (1994) 169-191. Zbl0820.35094MR1201239
  9. [9] Oleinik O.A., Discontinuous solutions of nonlinear differential equations, Transl. Amer. Math. Soc. Ser. 226 (1957) 95-172. MR151737
  10. [10] Triebel H., Fractals and Spectra Related to Fourier Analysis and Function Spaces, Monographs Math., 91, Birkhäuser, Basel, 1997. Zbl0898.46030MR1484417
  11. [11] Triebel H., Winkelvoss H., A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces, Studia Math.121 (2) (1996) 149-166. Zbl0864.46020MR1418396

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