TY - JOUR
T1 - Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations
AU - Cingolani, Silvia
AU - Degiovanni, Marco
AU - Sciunzi, Berardino
PY - 2024
Y1 - 2024
N2 - We establish critical groups estimates for the weak solutions of − Δ_p u = f(x, u) in Ω and u = 0 on ∂Ω via Morse index, where Ω is a bounded domain, f ∈ C^1(Ω×R) and f(x, s) > 0 for all x ∈ Ω, s > 0 and f(x, s) = 0 for all x ∈ Ω, s ≤ 0. The proof relies on new uniform Sobolev inequalities for approximating problems. We also prove critical groups estimates when Ω is the ball or the annulus and f is a sign changing function.
AB - We establish critical groups estimates for the weak solutions of − Δ_p u = f(x, u) in Ω and u = 0 on ∂Ω via Morse index, where Ω is a bounded domain, f ∈ C^1(Ω×R) and f(x, s) > 0 for all x ∈ Ω, s > 0 and f(x, s) = 0 for all x ∈ Ω, s ≤ 0. The proof relies on new uniform Sobolev inequalities for approximating problems. We also prove critical groups estimates when Ω is the ball or the annulus and f is a sign changing function.
KW - p-Laplace equations, critical groups, regularity theory, Sobolev embeddings
KW - p-Laplace equations, critical groups, regularity theory, Sobolev embeddings
UR - http://hdl.handle.net/10807/267554
UR - https://www.sciencedirect.com/science/article/pii/s002212362400034x
U2 - 10.1016/j.jfa.2024.110346
DO - 10.1016/j.jfa.2024.110346
M3 - Article
SN - 0022-1236
VL - 286
SP - N/A-N/A
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
ER -