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Boundary Trace for BV Functions in Regions with Irregular Boundary

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Analysis, Partial Differential Equations and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 193))

Abstract

The aim of this work is to generalize some results of [2] by Yu. Burago and V. Maz’ya for a wider class of regions with irregular boundaries.

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References

  1. F.J. Almgren, The theory of varifolds, Princeton, 1965 (preprint).

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  2. Yu. Burago, V. Maz’ya, Potential Theory and Function Theory for Irregular Regions, Consultants Bureau, New York, 1969.

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  3. H. Federer, Geometric measure theory, Springer, Berlin, 1969.

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  4. W.H. Fleming, R.W. Rishel, An integral formula for total gradient variation, Arch. Math. 11 (1960), 218–222.

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  5. V. Maz’ya, Sobolev spaces, Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1985.

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  6. V. Maz’ya, Classes of regions and embedding theorems for functional spaces, Dokl. Akad. Nauk SSSR 133 (1960), 527–530.

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  7. F. Morgan, Geometric Measure Theory: A Beginners Guide, third ed., Academic Press Inc., San Diego, CA 2000.

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Author information

Authors and Affiliations

  1. Saint-Petersburg branch of Steklov Math Institute, Fontanka 27, St. Petersburg, 191023, Russia

    Yuri Burago

  2. Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetsky prospekt, 28 Peterhof, St. Petersburg, 198504, Russia

    Nikolay N. Kosovsky

Authors
  1. Yuri Burago
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  2. Nikolay N. Kosovsky
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università della Basilicata, Viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Alberto Cialdea

  2. Dipartimento di Matematico “Guido Castelnuovo”, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Paolo Emilio Ricci  & Flavia Lanzara  & 

Additional information

To Vladimir Maz’ya on the occasion of his 70th birthday

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Burago, Y., Kosovsky, N.N. (2009). Boundary Trace for BV Functions in Regions with Irregular Boundary. In: Cialdea, A., Ricci, P.E., Lanzara, F. (eds) Analysis, Partial Differential Equations and Applications. Operator Theory: Advances and Applications, vol 193. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9898-9_2

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