TY - JOUR
T1 - Space quasiconformal composition operators with applications to Neumann eigenvalues
AU - Gol’dshtein, Vladimir
AU - Hurri-Syrjänen, Ritva
AU - Pchelintsev, Valerii
AU - Ukhlov, Alexander
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.
AB - In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.
KW - Elliptic equations
KW - Quasiconformal mappings
KW - Sobolev spaces
UR - http://www.scopus.com/inward/record.url?scp=85095699392&partnerID=8YFLogxK
U2 - 10.1007/s13324-020-00420-0
DO - 10.1007/s13324-020-00420-0
M3 - Article
AN - SCOPUS:85095699392
SN - 1664-2368
VL - 10
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 4
M1 - 78
ER -