Equivalence between regularity theorems and heat kernel estimates for higher-order elliptic operators and systems under divergence form

DOI10.1006/jfan.2000.3643zbMath0979.35044OpenAlexW1965709042MaRDI QIDQ1593735

Pascal Auscher, Mahmoud Qafsaoui

Publication date: 13 February 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3643

zbMATH Keywords

Morrey-Campanato spacesGårding inequalityGaussian upper boundslocal elliptic regularity

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Variational methods for higher-order elliptic equations (35J35)

Related Items

Calderón-Zygmund theory for non-integral operators and the \(H^\infty\) functional calculus, Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators, Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey, Perturbation and interpolation theorems for the \(H^\infty\)-calculus with applications to differential operators, Large time behavior for nonlinear higher order convection--diffusion equations, Maximal regularity properties of Agranovich-Vishik type abstract elliptic operators in the half-plane, Unnamed Item, Fractional Leibniz-type rules on spaces of homogeneous type, Gaussian estimates for heat kernels of higher order Schrödinger operators with potentials in generalized Schechter classes, Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms, Local Hardy spaces associated with inhomogeneous higher order elliptic operators, Size estimates of an obstacle in a stationary Stokes fluid, Convergence rates and interior estimates in homogenization of higher order elliptic systems, Characterizations of Hardy spaces associated to higher order elliptic operators, Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains, Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients, Global estimates for Green's matrix of second order parabolic systems with application to elliptic systems in two dimensional domains, The Neumann problem for higher order elliptic equations with symmetric coefficients, Regularity in oscillatory nonlinear elliptic systems, The Ẇ−1,p Neumann problem for higher order elliptic equations, Tent space well-posedness for parabolic Cauchy problems with rough coefficients, The \(L^p\) theory of divergence form elliptic operators under the Dirichlet condition, The \(L^p\) resolvents of second-order elliptic operators of divergence form under the Dirichlet condition, Explicit estimates on the fundamental solution of higher-order parabolic equations with measurable coefficients, Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces, Nonlinear elliptic equations with BMO coefficients in Reifenberg domains, Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients, Coincidence of weighted Hardy spaces associated with higher-order Schrödinger operators, Dirichlet and Neumann boundary values of solutions to higher order elliptic equations, The \(L ^{p}\) resolvents of elliptic operators with uniformly continuous coefficients.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limits on \(L^ p\) regularity of self-adjoint elliptic operators
• A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
• Complex multiplicative perturbations of elliptic operators: heat kernel bounds and holomorphic functional calculus
• Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold
• Uniformly elliptic operators with measurable coefficients
• Semigroup kernels, Poisson bounds, and holomorphic functional calculus
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Continuity of Solutions of Parabolic and Elliptic Equations
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• On Harnack's theorem for elliptic differential equations
• Heat kernels of multiplicative perturbations: Holder estimates and Gaussian lower bounds
• Heat kernel estimates and functional calculi of $-b \Delta$
• Regularity Theorems and Heat Kernel for Elliptic Operators
• Estimates on the generalized Morrey spaces L_{\phi^2,\lambda} and BMO_{\psi} for linear elliptic systems
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• Bounds for the fundamental solution of a parabolic equation