Decay Rate of L q Norms of Critical Schrödinger Heat Semigroups

DOI10.1007/978-88-470-2841-8_11zbMath1272.35034OpenAlexW175557470MaRDI QIDQ2841896

Yoshitsugu Kabeya, Kazuhiro Ishige

Publication date: 30 July 2013

Published in: Geometric Properties for Parabolic and Elliptic PDE's (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-88-470-2841-8_11

zbMATH Keywords

\(L^2-L^q\) estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Schrödinger operator, Schrödinger equation (35J10) Heat kernel (35K08)

Related Items

Large time behavior of solutions of the heat equation with inverse square potential, Sharp decay estimates of \(L^q\)-norms for nonnegative Schrödinger heat semigroups, Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups, Lp–Lq estimates for homogeneous operators

Cites Work

• Unnamed Item
• On criticality and ground states of second order elliptic equations. II
• \(L^p\) norms of nonnegative Schrödinger heat semigroup and the large time behavior of hot spots
• Positive solutions and large time behaviors of Schrödinger semigroups, Simon's problem
• Criticality and ground states for second-order elliptic equations
• Large time behaviors of hot spots for the heat equation with a potential
• Large time asymptotics for fundamental solutions of diffusion equations
• Structure of positive solutions to \((-\Delta +V)u=0\) in \(R^ n\)
• Large time behavior of the \(L^ p\) norm of Schrödinger semigroups
• \(L^ p\) norms of non-critical Schrödinger semigroups
• On positive solutions of second-order elliptic equations, stability results, and classification
• Global heat kernel bounds via desingularizing weights
• Harnack inequality and heat kernel estimates for the Schrödinger operator with Hardy potential
• Schrödinger semigroups
• Subcriticality and Gaugeability of the Schrodinger Operator
• Subcriticality, positivity, and gaugeability of the Schrödinger operator
• Parabolic Harnack inequality for the heat equation with inverse-square potential
• Global bounds of Schrödinger heat kernels with negative potentials