# Problems involving $p$-Laplacian type equations and measures

Mathematica Bohemica (2002)

- Volume: 127, Issue: 2, page 243-250
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topKilpeläinen, Tero. "Problems involving $p$-Laplacian type equations and measures." Mathematica Bohemica 127.2 (2002): 243-250. <http://eudml.org/doc/249064>.

@article{Kilpeläinen2002,

abstract = {In this paper I discuss two questions on $p$-Laplacian type operators: I characterize sets that are removable for Hölder continuous solutions and then discuss the problem of existence and uniqueness of solutions to $-\operatorname\{div\}(|\nabla u|^\{p-2\}\nabla u)=\mu $ with zero boundary values; here $\mu $ is a Radon measure. The joining link between the problems is the use of equations involving measures.},

author = {Kilpeläinen, Tero},

journal = {Mathematica Bohemica},

keywords = {$p$-Laplacian; removable sets; -Laplacian; removable sets},

language = {eng},

number = {2},

pages = {243-250},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Problems involving $p$-Laplacian type equations and measures},

url = {http://eudml.org/doc/249064},

volume = {127},

year = {2002},

}

TY - JOUR

AU - Kilpeläinen, Tero

TI - Problems involving $p$-Laplacian type equations and measures

JO - Mathematica Bohemica

PY - 2002

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 127

IS - 2

SP - 243

EP - 250

AB - In this paper I discuss two questions on $p$-Laplacian type operators: I characterize sets that are removable for Hölder continuous solutions and then discuss the problem of existence and uniqueness of solutions to $-\operatorname{div}(|\nabla u|^{p-2}\nabla u)=\mu $ with zero boundary values; here $\mu $ is a Radon measure. The joining link between the problems is the use of equations involving measures.

LA - eng

KW - $p$-Laplacian; removable sets; -Laplacian; removable sets

UR - http://eudml.org/doc/249064

ER -

## References

top- Function Spaces and Potential Theory, Springer, Berlin, 1995. (1995) MR1411441
- An ${L}^{1}$-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995), 241–273. (1995) MR1354907
- Nonlinear elliptic equations with right-hand side measures, Comm. Partial Diff. Eq. 17 (1992), 641–655. (1992) MR1163440
- Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), 539–551. (1996) MR1409661
- Selected Problems on Exceptional Sets, Van Nostrand, Princeton, N.Y., 1967. (1967) Zbl0189.10903MR0225986
- Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999), 741–808. (1999) MR1760541
- Removable sets for Lipschitz harmonic functions in the plane, Rev. Mat. Iberoam. 16 (2000), 137–215. (2000) MR1768535
- Uniqueness and maximal regularity for nonlinear elliptic systems of $n$-Laplace type with measure valued right hand side, J. Reine Angew. Math. 520 (2000), 1–35. (2000) MR1748270
- Inverting the $p$-harmonic operator, Manuscripta Math. 92 (1997), 249–258. (1997) MR1428651
- $A$-superharmonic functions and supersolutions of degenerate elliptic equations, Ark. Mat. 26 (1988), 87–105. (1988) MR0948282
- Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, Oxford, 1993. (1993) MR1207810
- Hölder continuity of solutions to quasilinear elliptic equations involving measures, Potential Analysis 3 (1994), 265–272. (1994)
- On the uniqueness problem for quasilinear elliptic equations involving measures, Rev. Mat. Iberoam. 12 (1996), 461–475. (1996)
- Removable sets for continuous solutions of quasilinear elliptic equations, (to appear). (to appear) MR1887015
- Regularity of solutions to some degenerate double obstacle problems, Indiana Univ. Math. J. 40 (1991), 1009–1028. (1991) Zbl0767.35029MR1129339
- On the Wolff potential and quasilinear elliptic equations involving measures, Ann. Acad. Sci. Fenn. Ser. A I. Math. Dissertationes 104 (1996), 1–71. (1996) Zbl0860.35041MR1386213
- Local behavior of solutions to quasi-linear equations, Acta Math. 111 (1964), 247–302. (1964) MR0170096
- Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa 18 (1964), 385–387. (1964) Zbl0142.37601MR0170094
- On the weak continuity of elliptic operators and applications to potential theory, (to appear). (to appear) MR1890997
- Dirichlet problems for quasilinear elliptic equations with measure data, Preprint.
- On nonhomogeneous quasilinear elliptic equations, Ann. Acad. Sci. Fenn. Math. Diss. 117 (1998). (1998) Zbl0911.35048MR1648847

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.