We consider the higher differentiability of solutions to the problem of minimizing
Keywords: Regularity of solutions to variational problems – p-harmonic functions – higher differentiability
@article{COCV_2017__23_4_1543_0, author = {Cellina, Arrigo}, title = {The regularity of solutions to some variational problems, including the $p${-Laplace} equation for $2 \leq{} p< 3$}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1543--1553}, publisher = {EDP-Sciences}, volume = {23}, number = {4}, year = {2017}, doi = {10.1051/cocv/2016064}, mrnumber = {3716932}, zbl = {1381.49015}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016064/} }
TY - JOUR AU - Cellina, Arrigo TI - The regularity of solutions to some variational problems, including the $p$-Laplace equation for $2 \leq{} p< 3$ JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1543 EP - 1553 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016064/ DO - 10.1051/cocv/2016064 LA - en ID - COCV_2017__23_4_1543_0 ER -
%0 Journal Article %A Cellina, Arrigo %T The regularity of solutions to some variational problems, including the $p$-Laplace equation for $2 \leq{} p< 3$ %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1543-1553 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016064/ %R 10.1051/cocv/2016064 %G en %F COCV_2017__23_4_1543_0
Cellina, Arrigo. The regularity of solutions to some variational problems, including the $p$-Laplace equation for $2 \leq{} p< 3$. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 4, pp. 1543-1553. doi : 10.1051/cocv/2016064. http://archive.numdam.org/articles/10.1051/cocv/2016064/
Estimates for solutions to equations of p-Laplace type in Ahlfors regular NTA-domains. J. Funct. Anal. 266 (2014) 5955–6005. | DOI | MR | Zbl
and ,A regularity classification of boundary points for p-harmonic functions and quasiminimizers. J. Math. Anal. Appl. 338 (2008) 39–47. | DOI | MR | Zbl
,Comparison Theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results. Inst. Henri Poincaré, Anal. Non Linéaire 15 (1998) 493–516. | DOI | Numdam | MR | Zbl
,A Liouville theorem for p-harmonic functions on exterior domains. Positivity 19 (2015) 577–586. | DOI | MR | Zbl
and ,A priori estimates for a class of quasi-linear elliptic equations. Trans. Amer. Math. Soc. 361 (2009) 6475–6500. | DOI | MR | Zbl
and ,Some remarks on the regularity of weak solutions of degenerate elliptic systems. Rev. Mat. Complutense 11 (1998) 203–219. | MR | Zbl
and ,E. Giusti, Metodi diretti nel calcolo delle variazioni. Unione Matematica Italiana, Bologna (1994). | MR | Zbl
Some regularity results for quasilinear elliptic systems of second order. Math. Z. 142 (1975) 67–86. | DOI | MR | Zbl
and ,Guide to nonlinear potential estimates. Bull. Math. Sci. 4 (2014) 1–82. | DOI | MR | Zbl
and ,O.A. Ladyzhenskaya and N.N. Uraltseva, Linear and quasilinear elliptic equations. Translated from the Russian. Academic Press, New York, London (1968). | Zbl
P. Lindqvist, Notes on the -Laplace equation, Lecture Notes at the University of Jyvaskyla. Department of Mathematics and Statistics (2006). | MR | Zbl
Nonlinear elliptic partial differential equations and p-harmonic functions on graphs. Differ. Integral Equ. 28 (2015) 79–102. | MR | Zbl
, and ,Estimates and existence of solutions of elliptic equations. Commun. Pure Appl. Math. 9 (1956) 509–529. | DOI | MR | Zbl
,On the Dirichlet problem for p-harmonic maps I: compact targets. Geom. Dedicata 177 (2015) 307–322. | DOI | MR | Zbl
and ,Regularity for a More General Class of Quasilinear Elliptic Equations. J. Differ. Equ. 51 (1984) 126–150. | DOI | MR | Zbl
,Regularity for a class of non-linear elliptic systems. Acta Math. 138 (1977) 219–240. | DOI | MR | Zbl
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