Wiener criterion for degenerate elliptic obstacle problem

Marco Biroli; Umberto Mosco

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1989)

  • Volume: 83, Issue: 1, page 63-67
  • ISSN: 1120-6330

Abstract

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We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the A 2 class.

How to cite

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Biroli, Marco, and Mosco, Umberto. "Wiener criterion for degenerate elliptic obstacle problem." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 63-67. <http://eudml.org/doc/287392>.

@article{Biroli1989,
abstract = {We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the $A_\{2\}$ class.},
author = {Biroli, Marco, Mosco, Umberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Variational inequalities; Potential theory; Regularity of weak solutions; continuity of obstacle problem; potential theory; regularity of weak solutions},
language = {eng},
month = {12},
number = {1},
pages = {63-67},
publisher = {Accademia Nazionale dei Lincei},
title = {Wiener criterion for degenerate elliptic obstacle problem},
url = {http://eudml.org/doc/287392},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Biroli, Marco
AU - Mosco, Umberto
TI - Wiener criterion for degenerate elliptic obstacle problem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 63
EP - 67
AB - We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the $A_{2}$ class.
LA - eng
KW - Variational inequalities; Potential theory; Regularity of weak solutions; continuity of obstacle problem; potential theory; regularity of weak solutions
UR - http://eudml.org/doc/287392
ER -

References

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  1. BIROLI, M. and MARCHI, S., 1986. Wiener estimates at boundary points for degenerate elliptic equations. Boll. U.M.I., 6, 5(B): 689-706; Correction, 1988, Boll. U.M.I., 2-B, 7: 713. Zbl0634.35034MR871695
  2. BIROLI, M. and MARCHI, S., 1989. Wiener estimates for degenerate elliptic equations II. Diff. Int. Eq., 2, 4: 511-523. Zbl0733.35045MR996757
  3. FABES, E., JERISON, D.S. and KENIG, C., 1982. The Wiener test for degenerate elliptic equations. Ann. Inst. Fourier, 3: 151-183. Zbl0488.35034MR688024
  4. FABES, E., KENIG, C. and SERAPIONI, R., 1982. The local regularity of solutions of degenerate elliptic equations. Comm. in PDE, 7, 1: 77-116. Zbl0498.35042MR643158DOI10.1080/03605308208820218
  5. FREHSE, J. and MOSCO, U., 1985. Wiener obstacles. In «Seminar on nonlinear partial differential equation», College de France, ed. by BREZIS H. and LIONS J.L., VI, Pitman. Zbl0583.35038MR772244
  6. LITTMAN, W., STAMPACCHIA, G. and WEINBERGER, H., 1963. Regular points for elliptc equations with discontinuous coefficients. Ann. Sc. Norm. Sup. Pisa, 17: 47-77. Zbl0116.30302MR161019
  7. MOSCO, U., 1987. Wiener criterion and potential estimates for the obstacle problem. Indiana Un. Math. J., 36: 455-494. Zbl0644.49005MR905606DOI10.1512/iumj.1987.36.36026

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