A Wiener type criterion for weighted quasiminima

Silvana Marchi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 1, page 25-28
  • ISSN: 1120-6330

Abstract

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We prove a sufficient condition of continuity at the boundary for quasiminima of degenerate type. W. P. Ziemer stated a Wiener-type criterion for the quasiminima defined by Giaquinta and Giusti. In this paper we extend the result of Ziemer to the case of weighted quasiminima, the weight being in the A 2 class of Muckenhoupt.

How to cite

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Marchi, Silvana. "A Wiener type criterion for weighted quasiminima." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.1 (1991): 25-28. <http://eudml.org/doc/244188>.

@article{Marchi1991,
abstract = {We prove a sufficient condition of continuity at the boundary for quasiminima of degenerate type. W. P. Ziemer stated a Wiener-type criterion for the quasiminima defined by Giaquinta and Giusti. In this paper we extend the result of Ziemer to the case of weighted quasiminima, the weight being in the \(A^\{2\}\) class of Muckenhoupt.},
author = {Marchi, Silvana},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Wiener criterion; Degenerate quasiminima; Weights in the A\_2 class of Muckenhoupt; degenerate quasiminima; Caratheodory function; sufficient condition for continuity; Harnack inequality},
language = {eng},
month = {3},
number = {1},
pages = {25-28},
publisher = {Accademia Nazionale dei Lincei},
title = {A Wiener type criterion for weighted quasiminima},
url = {http://eudml.org/doc/244188},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Marchi, Silvana
TI - A Wiener type criterion for weighted quasiminima
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/3//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 1
SP - 25
EP - 28
AB - We prove a sufficient condition of continuity at the boundary for quasiminima of degenerate type. W. P. Ziemer stated a Wiener-type criterion for the quasiminima defined by Giaquinta and Giusti. In this paper we extend the result of Ziemer to the case of weighted quasiminima, the weight being in the \(A^{2}\) class of Muckenhoupt.
LA - eng
KW - Wiener criterion; Degenerate quasiminima; Weights in the A_2 class of Muckenhoupt; degenerate quasiminima; Caratheodory function; sufficient condition for continuity; Harnack inequality
UR - http://eudml.org/doc/244188
ER -

References

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  2. COIFMAN, R. - FEFFERMAN, C., Weighted norm inequalities for maximal functions and singular integrals. Studia Math., LI, 1974, 241-250. Zbl0291.44007MR358205
  3. BIROLI, M. - MARCHI, S., Wiener estimates for degenerate elliptic equations. II. Differential and Integral Equations, vol. 2, n. 4, 1989, 511-523. Zbl0733.35045MR996757
  4. DI BENEDETTO, E. - TRUDINGER, N. S., Harnack inequalities for quasi-minima of variational integrals. Ann. Inst. H. Poincaré, Anal. Non Linéaire, vol. 1, n. 4, 1984, 295-308. Zbl0565.35012MR778976
  5. GIAQUINTA, M. - GIUSTI, E., On the regularity of the minima of variationals integrals. Acta Math., 148, 1982, 31-46. Zbl0494.49031MR666107DOI10.1007/BF02392725
  6. GIAQUINTA, M. - GIUSTI, E., Quasiminima. Ann. Inst. H. Poincaré, Anal. Non Linéaire, 1 (2), 1984, 79-107. Zbl0541.49008MR778969
  7. IVERT, P. A., Continuity of quasiminima under the presence of irregular obstacles. Partial Differential Equations, vol. 19, 1987, 155-167. MR1055168
  8. MUCKENHOUPT, B., Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc., 165, 1972, 207-226. Zbl0236.26016MR293384
  9. MARCHI, S., Boundary regularity for weighted quasiminima. Riv. Mat. Univ. Parma, 15 (4), 1989, in press. Zbl0954.49023MR1121007
  10. MARCHI, S., Boundary regularity for weighted quasiminima. II. Nonlinear Anal., submitted. Zbl0901.49031
  11. MEYERS, N. G., A theory of capacities for potentials of functions in Lebesgue classes. Math. Scand., 26, 1970, 255-292. Zbl0242.31006MR277741
  12. MURTHY, M. K. V. - STAMPACCHIA, G., Boundary value problems for some degenerate elliptic operators. Ann. Mat. Pura Appl, 80, 1968, 1-122. Zbl0185.19201MR249828
  13. ZIEMER, W. P., Boundary regularity for quasiminima. Arch. Rational Mech. Anal., 92, 1986, 371-382. Zbl0611.35030MR823124DOI10.1007/BF00280439

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