On \(L^p\)-contractivity of semigroups generated by linear partial differential operators

DOI10.1006/JFAN.1999.3393zbMath0933.47027OpenAlexW1981526371MaRDI QIDQ1294096

Mikael Lange, Vladimir Gilelevich Maz'ya

Publication date: 27 March 2000

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

Full work available at URL: https://doi.org/10.1006/jfan.1999.3393

zbMATH Keywords

generatorCauchy problemdissipativityelliptic operatorcontraction semigrouplinear partial differential operatorcomplex and real \(L^p\)-spacesorder of operator

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) One-parameter semigroups and linear evolution equations (47D06) General theory of partial differential operators (47F05)

Related Items (12)

Higher-order operators on networks: hyperbolic and parabolic theory ⋮ A survey of functional and Lp-dissipativity theory ⋮ Nonlinear nonlocal Douglas identity ⋮ Characterizations of Hardy spaces associated to higher order elliptic operators ⋮ Riesz transforms associated with higher-order Schrödinger type operators ⋮ Schrödinger and polyharmonic operators on infinite graphs: parabolic well-posedness and \(p\)-independence of spectra ⋮ Gaussian bounds for higher-order elliptic differential operators with Kato type potentials ⋮ Progress in the Problem of the L p -Contractivity of Semigroups for Partial Differential Operators ⋮ Optimal Hardy inequality for the fractional Laplacian on \(L^p\) ⋮ A note on maximal estimates for stochastic convolutions ⋮ Criterion for the \(L^p\)-dissipativity of second order differential operators with complex coefficients ⋮ Some remarks on operator-norm convergence of the Trotter product formula on Banach spaces.

Cites Work

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• Dual semigroups and second order linear elliptic boundary value problems
• Analysis of the Laplacian on a complete Riemannian manifold
• \(L^ p\) contractive projections and the heat semigroup for differential forms
• A note on fractional derivatives of semigroups and cosine functions
• Criteria for validity of the maximum modulus principle for solutions of linear parabolic systems
• Semi-linear second-order elliptic equations in \(L^1\)

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