TY - UNPB
T1 - Principal frequencies of free non-homogeneous membranes and Sobolev extension operators
AU - Gol'dshtein, Vladimir
AU - Pchelintsev, Valerii
AU - Ukhlov, Alexander
N1 - 10 pages
PY - 2021/12/26
Y1 - 2021/12/26
N2 - Using the quasiconformal mappings theory and Sobolev extension operators, we obtain estimates of principal frequencies of free non-homogeneous membranes. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. Free non-homogeneous membranes we consider as circular membranes in the quasiconformal geometry associated with non-homogeneity of membranes. As a consequence we get a connection between principal frequencies of free membranes and the smallest-circle problem (initially suggested by J.~J. Sylvester in 1857).
AB - Using the quasiconformal mappings theory and Sobolev extension operators, we obtain estimates of principal frequencies of free non-homogeneous membranes. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. Free non-homogeneous membranes we consider as circular membranes in the quasiconformal geometry associated with non-homogeneity of membranes. As a consequence we get a connection between principal frequencies of free membranes and the smallest-circle problem (initially suggested by J.~J. Sylvester in 1857).
KW - math.AP
KW - 35P15, 46E35, 30C65
U2 - 10.48550/arXiv.2112.13371
DO - 10.48550/arXiv.2112.13371
M3 - Preprint
BT - Principal frequencies of free non-homogeneous membranes and Sobolev extension operators
ER -