Degenerate elliptic equations with measure data and nonlinear potentials

Tero Kilpeläinen; Jan Malý

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1992)

  • Volume: 19, Issue: 4, page 591-613
  • ISSN: 0391-173X

How to cite

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Kilpeläinen, Tero, and Malý, Jan. "Degenerate elliptic equations with measure data and nonlinear potentials." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 19.4 (1992): 591-613. <http://eudml.org/doc/84138>.

@article{Kilpeläinen1992,
author = {Kilpeläinen, Tero, Malý, Jan},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {-superharmonic functions; right hand side measure; upper and lower estimates for the solutions},
language = {eng},
number = {4},
pages = {591-613},
publisher = {Scuola normale superiore},
title = {Degenerate elliptic equations with measure data and nonlinear potentials},
url = {http://eudml.org/doc/84138},
volume = {19},
year = {1992},
}

TY - JOUR
AU - Kilpeläinen, Tero
AU - Malý, Jan
TI - Degenerate elliptic equations with measure data and nonlinear potentials
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1992
PB - Scuola normale superiore
VL - 19
IS - 4
SP - 591
EP - 613
LA - eng
KW - -superharmonic functions; right hand side measure; upper and lower estimates for the solutions
UR - http://eudml.org/doc/84138
ER -

References

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  2. [2] R. Gariepy - W.P. Ziemer, A regularity condition at the boundary for solutions of quasilinear elliptic equations, Arch. Rational Mech. Anal.67 (1977), 25-39. Zbl0389.35023MR492836
  3. [3] L.I. Hedberg - Th H. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier, Grenoble33,4 (1983), 161-187. Zbl0508.31008MR727526
  4. [4] J. Heinonen - T. Kilpeläinen, A-superharmonic functions and supersolutions of degenerate elliptic equations, Ark. Mat.26 (1988), 87-105. Zbl0652.31006MR948282
  5. [5] J. Heinonen - T. Kilpeläinen, Polar sets for supersolutions of degenerate elliptic equations, Math. Scand.63 (1988), 136-150. Zbl0706.31015MR994974
  6. [6] J. Heinonen - T. Kilpeläinen, On the Wiener criterion and quasilinear obstacle problems, Trans. Amer. Math. Soc.310 (1988), 239-255. Zbl0711.35052MR965751
  7. [7] J. Heinonen - T. Kilpeläinen - J. Malý, Connectedness in fine topologies, Ann. Acad. Sci. Fenn. Ser. A I Math.15 (1990); 107-123. Zbl0715.31005MR1050785
  8. [8] J. Heinonen - T. Kilpeläinen - O. Martio, Fine topology and quasilinear elliptic equations, Ann. Inst. Fourier, Grenoble39,2 (1989), 293-318. Zbl0659.35038MR1017281
  9. [9] J. Heinonen - T. Kilpeläinen - O. Martio, Nonlinear potential theory of degenerate elliptic equations, Oxford University Press (in press). Zbl0776.31007MR1207810
  10. [10] T. Kilpeläinen, Potential theory for supersolutions degenerate elliptic equations, Indiana Univ. Math. J.38 (1989), 253-275. Zbl0688.31005MR997383
  11. [11] P. Lindqvist, On the definition and properties of p-superharmonic functions, J. Reine Angew. Math.365 (1986), 67-79. Zbl0572.31004MR826152
  12. [12] P. Lindqvist - O. Martio, Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math.155 (1985), 153-171. Zbl0607.35042MR806413
  13. [13] V.G. Maz'ya, On the continuity at a boundary point of solutions of quasi-linear elliptic equations, Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 25 (1970), 42-55 (Russian), Vestnik Leningrad Univ. Math.3, (1976), 225-242. (English translation). Zbl0252.35024MR274948
  14. [14] J.M. Rakotoson, Equivalence between the growth of f |∇u| pdy and T in the equation P[u]=T, J. Differential Equation86 (1990), 102-122. Zbl0707.35033
  15. [15] J.M. Rakotoson - W.P. Ziemer, Local behavior of solutions of quasilinear elliptic equations with general structure, Trans. Amer. Math. Soc.319 (1990), 747-764. Zbl0708.35023MR998128
  16. [16] J. Serrin, Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (1964), 385-387. Zbl0142.37601MR170094
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Citations in EuDML Documents

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  1. Juha Kinnunen, Peter Lindqvist, Summability of semicontinuous supersolutions to a quasilinear parabolic equation
  2. Darko Žubrinić, Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential
  3. Jan Malý, Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points
  4. Tadeusz Iwaniec, Carlo Sbordone, Quasiharmonic fields
  5. Tadeusz Iwaniec, Nonlinear analysis and quasiconformal mappings from the perspective of PDEs
  6. Tadeusz Iwaniec, Carlo Sbordone, Caccioppoli estimates and very weak solutions of elliptic equations
  7. Giuseppe Mingione, La teoria di Calderón-Zygmund dal caso lineare a quello non lineare

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