Criteria for the \(L^p\)-dissipativity of systems of second order differential equations

DOI10.1007/s11587-006-0014-xzbMath1189.47043arXivmath/0602382OpenAlexW1612937145MaRDI QIDQ997611

Alberto Cialdea, Vladimir Gilelevich Maz'ya

Publication date: 7 August 2007

Published in: Ricerche di Matematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602382

zbMATH Keywords

algebraic conditionselasticity system\(L^p\)-dissipativity

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) General theory of partial differential operators (47F05) Dynamical problems in solid mechanics (74H99) Linear accretive operators, dissipative operators, etc. (47B44) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (max. 100)

On the \(L^p\)-theory of vector-valued elliptic operators ⋮ Regularity theory for solutions to second order elliptic operators with complex coefficients and the \(L^{p}\) Dirichlet problem ⋮ Spectral analysis of localized rotating waves in parabolic systems ⋮ A survey of functional and Lp-dissipativity theory ⋮ The functional dissipativity of certain systems of partial differential equations ⋮ Criterion for the functional dissipativity of the Lamé operator ⋮ Boundary value problems for second-order elliptic operators with complex coefficients ⋮ The \(p\)-ellipticity condition for second order elliptic systems and applications to the Lamé and homogenization problems ⋮ Criterion for the functional dissipativity of second order differential operators with complex coefficients ⋮ A new \(L^{p}\)-antieigenvalue condition for Ornstein-Uhlenbeck operators ⋮ The -dissipativity of first order partial differential operators ⋮ Progress in the Problem of the L p -Contractivity of Semigroups for Partial Differential Operators ⋮ Resolvent Estimates for Non-Selfadjoint Operators via Semigroups ⋮ On the \(\mathrm{L}^p\)-theory for second-order elliptic operators in divergence form with complex coefficients ⋮ The 𝐿^{𝑝}-dissipativity of certain differential and integral operators

Cites Work

• Unnamed Item
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• Unnamed Item
• Dual semigroups and second order linear elliptic boundary value problems
• \(L^ p\) contractive projections and the heat semigroup for differential forms
• Singular perturbation and boundary layer for an abstract Cauchy problem
• Elliptic differential operators on Lie groups
• Criteria for validity of the maximum modulus principle for solutions of linear parabolic systems
• Semi-linear second-order elliptic equations in \(L^1\)
• On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. I
• On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. II
• Uniformly elliptic operators with measurable coefficients
• On \(C_ 0\)-semigroups generated by elliptic second order differential expressions on \(L^ p\)-spaces
• Absence of \(L^\infty\)-contractivity for semigroups associated to complex elliptic operators in divergence form
• \(L^p\)-theory for elliptic operators on \(\mathbb R^d\) with singular coefficients
• Linear elliptic differential systems and eigenvalue problems
• Criterion for the \(L^p\)-dissipativity of second order differential operators with complex coefficients
• Sectorialness of Second Order Elliptic Operators in Divergence Form
• $C_0$-Semigroups in $L^p ({\bf R}^d )$ and $\widehat{C}({\bf R}^d )$ Spaces Generated by the Differential Expression $\Delta + b \cdot \nabla$
• L ^p Spectral Independence and L ¹ Analyticity
• Gaussian estimates for second-order operators with unbounded coefficients

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