On general solvability properties of p -Lapalacian-like equations

Pavel Drábek; Christian G. Simader

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 1, page 103-122
  • ISSN: 0862-7959

Abstract

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We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation - Δ p u = f in Ω , where Ω is a very general domain in ℝ N , including the case Ω = ℝ N .

How to cite

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Drábek, Pavel, and Simader, Christian G.. "On general solvability properties of $p$-Lapalacian-like equations." Mathematica Bohemica 127.1 (2002): 103-122. <http://eudml.org/doc/249018>.

@article{Drábek2002,
abstract = {We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation \[ -\Delta \_p u = f \ \text\{in\} \ \Omega , \] where $\Omega $ is a very general domain in $\mathbb \{R\}^N$, including the case $\Omega = \mathbb \{R\}^N$.},
author = {Drábek, Pavel, Simader, Christian G.},
journal = {Mathematica Bohemica},
keywords = {quasilinear elliptic equations; weak solutions; solvability; quasilinear elliptic equations; weak solutions; solvability; existence; uniqueness},
language = {eng},
number = {1},
pages = {103-122},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On general solvability properties of $p$-Lapalacian-like equations},
url = {http://eudml.org/doc/249018},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Drábek, Pavel
AU - Simader, Christian G.
TI - On general solvability properties of $p$-Lapalacian-like equations
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 1
SP - 103
EP - 122
AB - We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation \[ -\Delta _p u = f \ \text{in} \ \Omega , \] where $\Omega $ is a very general domain in $\mathbb {R}^N$, including the case $\Omega = \mathbb {R}^N$.
LA - eng
KW - quasilinear elliptic equations; weak solutions; solvability; quasilinear elliptic equations; weak solutions; solvability; existence; uniqueness
UR - http://eudml.org/doc/249018
ER -

References

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  1. Solvability and Bifurcations of Nonlinear Equations, Pitman Research Notes in Mathematics Series 264, Longman, 1992. (1992) MR1175397
  2. Quasilinear Elliptic Equations with Degenerations and Singularities, de Gruyter Series in Nonlinear Analysis and Applications 5, Walter de Gruyter, Berlin, 1997. (1997) MR1460729
  3. 10.1002/mana.1999.3212030102, Math. Nachrichten 203 (1999), 5–30. (1999) MR1698637DOI10.1002/mana.1999.3212030102
  4. Nonlinear Differential Equations, Elsevier, Amsterdam, 1980. (1980) MR0558764
  5. Spectral Analysis of Nonlinear Operators, Lecture Notes in Mathematics 346, Springer, Berlin, 1973. (1973) MR0467421
  6. Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. (1977) MR0473443
  7. Sur la non résolubilité du p -laplacien C.R, Acad. Sci. Paris, t. 326, Sér. I (1998), 1185–1187. (1998) MR1650266
  8. Function Spaces, Academia, Praha, 1977. (1977) MR0482102
  9. A second look on definition and equivalent norms of Sobolev spaces, Math. Bohem. 124 (1999), 315–328. (1999) Zbl0941.46019MR1780700
  10. Les méthodes directes en théorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
  11. Sobolev’s original definition of his spaces revisited and a comparison with nowadays definition, Le Matematiche 54 (1999), 149–178. (1999) Zbl0947.46022MR1749828
  12. The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains, Pitman Research Notes in Mathematics Series 360, Addison Wesley Longman, 1996. (1996) MR1454361

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