Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms

Salvatore Bonafede

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 1, page 45-64
  • ISSN: 0010-2628

Abstract

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We prove the local Hölder continuity of bounded generalized solutions of the Dirichlet problem associated to the equation ∑ i = 1 m ∂ ∂ x i a i ( x , u , ∇ u ) - c 0 | u | p - 2 u = f ( x , u , ∇ u ) , assuming that the principal part of the equation satisfies the following degenerate ellipticity condition λ ( | u | ) ∑ i = 1 m a i ( x , u , η ) η i ≥ ν ( x ) | η | p , and the lower-order term f has a natural growth with respect to ∇ u .

How to cite

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Bonafede, Salvatore. "Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms." Commentationes Mathematicae Universitatis Carolinae 59.1 (2018): 45-64. <http://eudml.org/doc/294252>.

@article{Bonafede2018,
abstract = {We prove the local Hölder continuity of bounded generalized solutions of the Dirichlet problem associated to the equation $\sum _\{i =1\}^\{m\} \frac\{\partial \}\{\partial x_i\} a_i (x, u, \nabla u) - c_0 |u|^\{p-2\} u = f(x, u, \nabla u),$ assuming that the principal part of the equation satisfies the following degenerate ellipticity condition $\lambda (|u|) \sum _\{i=1\}^m a_i (x,u, \eta ) \eta _i \ge \nu (x) |\eta |^p,$ and the lower-order term $f$ has a natural growth with respect to $\nabla u$.},
author = {Bonafede, Salvatore},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {elliptic equations; weight function; regularity of solutions},
language = {eng},
number = {1},
pages = {45-64},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms},
url = {http://eudml.org/doc/294252},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Bonafede, Salvatore
TI - Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 1
SP - 45
EP - 64
AB - We prove the local Hölder continuity of bounded generalized solutions of the Dirichlet problem associated to the equation $\sum _{i =1}^{m} \frac{\partial }{\partial x_i} a_i (x, u, \nabla u) - c_0 |u|^{p-2} u = f(x, u, \nabla u),$ assuming that the principal part of the equation satisfies the following degenerate ellipticity condition $\lambda (|u|) \sum _{i=1}^m a_i (x,u, \eta ) \eta _i \ge \nu (x) |\eta |^p,$ and the lower-order term $f$ has a natural growth with respect to $\nabla u$.
LA - eng
KW - elliptic equations; weight function; regularity of solutions
UR - http://eudml.org/doc/294252
ER -

References

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