Algebra properties for Sobolev spaces -- applications to semilinear PDEs on manifolds

DOI10.1007/s11854-012-0043-1zbMath1286.46033arXiv1107.3826OpenAlexW2087679909MaRDI QIDQ355969

Emmanuel Russ, Nadine Badr, Frédéric Bernicot

Publication date: 25 July 2013

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3826

zbMATH Keywords

Sobolev spaceRiemannian manifoldheat semigroupBessel potential

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Functional calculus for linear operators (47A60) Groups and semigroups of linear operators (47D03) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Elliptic equations on manifolds, general theory (58J05)

Related Items (11)

Heat semigroup and singular PDEs. With an appendix by F. Bernicot and D. Frey ⋮ Homogeneous algebras via heat kernel estimates ⋮ Is there proof that backreaction of inhomogeneities is irrelevant in cosmology? ⋮ Besov and Triebel-Lizorkin spaces on Lie groups ⋮ Propagation of low regularity for solutions of nonlinear PDEs on a riemannian manifold with a sub-Laplacian structure ⋮ A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces ⋮ Sobolev spaces on Lie groups: embedding theorems and algebra properties ⋮ Pseudodifferential operators associated with a semigroup of operators ⋮ Sobolev algebras through heat kernel estimates ⋮ Well-posedness and scattering for the mass-energy NLS on \(\mathbb{R}^n\times\mathcal{M}^k\) ⋮ Sobolev algebras on nonunimodular Lie groups

Cites Work

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• \(L^p\) self-improvement of generalized Poincaré inequalities in spaces of homogeneous type
• On the energy critical Schrödinger equation in 3D non-trapping domains
• Le calcul fonctionnel dans les espaces de Sobolev. (Functional calculus in Sobolev spaces)
• Hardy spaces of differential forms on Riemannian manifolds
• New abstract Hardy spaces
• Hardy and BMO spaces associated to divergence form elliptic operators
• Balls and metrics defined by vector fields. I: Basic properties
• Brownian motion on the Sierpinski gasket
• Fractional powers of dissipative operators
• Brownian motion on a homogeneous fractal
• Estimates of transition densities for Brownian motion of nested fractals
• Heat kernels of second order complex elliptic operators and applications
• Analysis on Lie groups with polynomial growth
• Heat kernel of complex elliptic operators
• Parabolic Harnack inequality for divergence form second order differential operators
• Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs
• The Poincaré inequality is an open ended condition
• Propagation of low regularity for solutions of nonlinear PDEs on a riemannian manifold with a sub-Laplacian structure
• Stability of parabolic Harnack inequalities on metric measure spaces
• Non-linear semi-groups
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Sobolev algebras on Lie groups and Riemannian manifolds
• A 𝑇(1)-theorem in relation to a semigroup of operators and applications to new paraproducts
• THE HEAT EQUATION ON NONCOMPACT RIEMANNIAN MANIFOLDS
• The conservation property of the heat equation on riemannian manifolds
• On necessary and sufficient conditions for 𝐿^{𝑝}-estimates of Riesz transforms associated to elliptic operators on ℝⁿ and related estimates
• A Characterization of Potential Spaces
• Commutator estimates and the euler and navier-stokes equations
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Riesz transforms for $1\le p\le 2$
• Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case 1<s<n/p
• Necessary conditions on composition operators acting between Besov spaces. The case 1 < s < n/p. III
• Besov algebras on Lie groups of polynomial growth
• Abstract framework for John-Nirenberg inequalities and applications to Hardy spaces
• Self-improving properties for abstract Poincaré type inequalities
• Duality of Hardy and BMO spaces associated with operators with heat kernel bounds
• The characterization of functions arising as potentials
• Second order elliptic operators with complex bounded measurable coefficients in $L^p$, Sobolev and Hardy spaces
• Exact smoothing properties of Schrodinger semigroups
• New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications
• Limiting case of the Sobolev inequality in BMO, with application to the Euler equations

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