Second Order Elliptic Integro-Differential Problems

By M. G. Garroni, José-Luis Menaldi. 2002

148 citations recorded by the source corpus.

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In Numerical Analysis

Citations in the corpus

Boundary Harnack principle for Δ+Δ^{/2} (2012, result): “For earlier results on second order integro-difierential operators, one can see [ 24 ] and the references therein.”
On Neumann Type Problems for nonlocal Equations set in a half Space (2011, methodology): “(ii) In [16], Dirichlet type problems are considered, and the authors have to assume extra decay properties of the jump vector η near the boundary, conditions that are not satisﬁed in our Neumann models.”
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models (2005, background): “3 Viscosity solutions Existence and uniqueness of (classical) solutions for the PIDEs considered above in Sobolev / Hölder spaces have been studied in [6, 16] in the case where the”
A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations (2006, methodology): “We refer to [18, 19] for a deep investigation of integro-PDEs in the framework of Green functions and regular solutions, see also [20].”
A Faber-Krahn inequality for mixed local and nonlocal operators (2021, methodology): “1For instance, in the most delicate case s ∈ [1/2, 1), one can use the setting in [35] with j(x, ξ) := ξ, m(x, ξ) := 1, π(dξ) := |ξ|−n−2s dξ, j(ξ) := ξ, γ := 2s + (with > 0 conveniently small), θ := 0, γ1 := γ and λ1(ξ) := |ξ| .”
CONTINUOUS DEPENDENCE ESTIMATES FOR VISCOSITY SOLUTIONS OF INTEGRO-PDES (2005, unknown): “We refer to the books [28, 29] for an investigation of integro-PDEs by completely different methods.”
Lipschitz regularity of solutions for mixed integro-differential equations (2011, methodology): “For results in the framework of Green functions and classical solutions we send the reader to the up-to-date book of Garroni and Menaldi [9] and the references therein.”
Second-order elliptic integro-differential equations: viscosity solutions' theory revisited (2007, background): “To finish with, operators of the form (15) are probably the most general ones and they appear for instance in [10].”
On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations (2008, methodology): “Such problems have been already addressed by using different theory: we refer to Bony, Courrège and Priouret [6] for a semigroup approach and to Garroni and Menaldi [11] for a classical PDE approach using Sobolev spaces.”