On the continuity of minimizers for quasilinear functionals

David Cruz-Uribe; Patrizia Di Gironimo; Luigi D'Onofrio

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 1, page 111-116
  • ISSN: 0011-4642

Abstract

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In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by log log ( 1 / | x | ) - 1 . Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 103–116.

How to cite

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Cruz-Uribe, David, Di Gironimo, Patrizia, and D'Onofrio, Luigi. "On the continuity of minimizers for quasilinear functionals." Czechoslovak Mathematical Journal 62.1 (2012): 111-116. <http://eudml.org/doc/246774>.

@article{Cruz2012,
abstract = {In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by $\log \log (1/|x|)^\{-1\}$. Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 103–116.},
author = {Cruz-Uribe, David, Di Gironimo, Patrizia, D'Onofrio, Luigi},
journal = {Czechoslovak Mathematical Journal},
keywords = {regularity; quasilinear functionals; calculus of variations; regularity; quasilinear functional; calculus of variations},
language = {eng},
number = {1},
pages = {111-116},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the continuity of minimizers for quasilinear functionals},
url = {http://eudml.org/doc/246774},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Cruz-Uribe, David
AU - Di Gironimo, Patrizia
AU - D'Onofrio, Luigi
TI - On the continuity of minimizers for quasilinear functionals
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 111
EP - 116
AB - In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by $\log \log (1/|x|)^{-1}$. Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 103–116.
LA - eng
KW - regularity; quasilinear functionals; calculus of variations; regularity; quasilinear functional; calculus of variations
UR - http://eudml.org/doc/246774
ER -

References

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  1. Fusco, N., Hutchinson, J. E., 10.1017/S1446788700037496, J. Aust. Math. Soc., Ser. A 57 (1994), 158-169. (1994) Zbl0864.35032MR1288671DOI10.1017/S1446788700037496
  2. Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order. Reprint of the 1998 ed, Classics in Mathematics. Springer, Berlin (2001). (2001) Zbl1042.35002MR1814364
  3. Manfredi, J. J., 10.1007/BF02921588, J. Geom. Anal. 4 (1994), 393-402. (1994) Zbl0805.35013MR1294334DOI10.1007/BF02921588
  4. Morrey, C. B., 10.1090/S0002-9947-1938-1501936-8, Trans. Am. Math. Soc. 43 (1938), 126-166. (1938) Zbl0018.40501MR1501936DOI10.1090/S0002-9947-1938-1501936-8
  5. Morrey, C. B., Multiple integral problems in the calculus of variations and related topics, Univ. California Publ. Math., n. Ser. 1 (1943), 1-130. (1943) Zbl0063.04107MR0011537
  6. Onninen, J., Zhong, X., Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 6 (2007), 103-116. (2007) Zbl1150.35055MR2341517

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