On a degenerate heat equation with a singular potential
From MaRDI portal
Publication:5955071
DOI10.1006/jfan.2001.3792zbMath1056.35093OpenAlexW2081976854MaRDI QIDQ5955071
Jerome A. Goldstein, Qi S. Zhang
Publication date: 2001
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jfan.2001.3792
Degenerate parabolic equations (35K65) Analysis on real and complex Lie groups (22E30) Analyticity in context of PDEs (35A20)
Related Items
Doubly Nonlinear Degenerate Parabolic Equations with a Singular Potential for Greiner Vector Fields ⋮ The heat equation with singular potentials. II: Hypoelliptic case ⋮ Hardy-type inequalities derived from \(p\)-harmonic problems ⋮ Some nonlinear equations of the nonstable filtration type and embedding theorems ⋮ The linear heat equation with highly oscillating potential ⋮ Heat equation with a singular potential on the boundary and the Kato inequality ⋮ Existence of solutions to a nonlinear parabolic problem with two weights ⋮ Unnamed Item ⋮ Rellich type inequalities related to Grushin type operators and Greiner type operators ⋮ SOME -HARDY AND -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS ⋮ Non-existence results for \(p \)-Laplacian parabolic problems on the Heisenberg group \(\mathbb{H}^n \) ⋮ Local logarithmic stability of an inverse coefficient problem for a singular heat equation with an inverse-square potential ⋮ Null controllability for the heat equation with singular inverse-square potentials ⋮ Regularity criteria of the axisymmetric Navier-Stokes equations and Hardy-Sobolev inequality in mixed Lorentz spaces ⋮ Nonnegative solutions of an elliptic equation with a singular potential ⋮ On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces ⋮ Hardy-Sobolev type inequalities with sharp constants in Carnot-Carathéodory spaces ⋮ Doubly nonlinear parabolic equations with singular lower order term. ⋮ On nonexistence of Baras-Goldstein type without positivity assumptions for singular linear and nonlinear parabolic equations ⋮ Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups ⋮ Hardy type inequalities related to Carnot-Carathéodory distance on the Heisenberg group ⋮ Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential ⋮ The Hardy inequality and nonlinear parabolic equations on Carnot groups ⋮ Quasilinear parabolic and elliptic equations with singular potentials ⋮ Hardy inequalities resulted from nonlinear problems dealing with \(A\)-Laplacian ⋮ Weighted Hardy and Rellich inequality on Carnot groups ⋮ Some weighted Hardy-type inequalities on anisotropic Heisenberg groups ⋮ On nonexistence of Baras–Goldstein type for higher-order parabolic equations with singular potentials ⋮ Long-time behavior of solutions of some doubly nonlinear equation ⋮ Hardy inequalities related to Grushin type operators ⋮ Nonlinear parabolic equations with singular coefficient and critical exponent ⋮ On the nonexistence of positive solutions to nonlinear degenerate parabolic equations with singular coefficients ⋮ The null controllability for a singular heat equation with variable coefficients ⋮ Nonexistence results for parabolic equations involving the \(p\)-Laplacian and Hardy-Leray-type inequalities on Riemannian manifolds ⋮ Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation ⋮ Existence of nonnegative solutions for a fractional parabolic equation in the entire space ⋮ A parabolic equation for the fractional Laplacian in the entire space: blow-up of nonnegative solutions ⋮ A MATHEMATICAL MODEL FOR THE USE OF ENERGY RESOURCES: A SINGULAR PARABOLIC EQUATION ⋮ Instantaneous blowup and singular potentials on Heisenberg groups ⋮ Nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities ⋮ Linear parabolic equations with strong singular potentials
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Uniformly elliptic operators on Riemannian manifolds
- Frequency functions on the Heisenberg group and the uncertainty principle and unique continuation
- On the parabolic kernel of the Schrödinger operator
- Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
- Hardy inequalities and some critical elliptic and parabolic problems
- The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
- The Heat Equation with a Singular Potential
- Global Behavior of the Cauchy Problem for Some Critical Nonlinear Parabolic Equations
- Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier
