Spectral decomposition of Green's integrals and existence of \(W^{s,2}\)-solutions of matrix factorizations of the Laplace operator in a ball

zbMath0955.35017MaRDI QIDQ1356834

Alexandre A. Shlapunov

Publication date: 4 March 2001

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=RSMUP_1996__96__237_0

zbMATH Keywords

fundamental solutionsolvabilityharmonic functionsGreen's integral

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fundamental solutions to PDEs and systems of PDEs with constant coefficients (35E05)

Related Items

On the approximation of solutions to the heat equation in the Lebesgue class \(L^2\) by more regular solutions ⋮ Unnamed Item ⋮ A class of Toeplitz operators in several variables ⋮ Sturm–Liouville problems in weighted spaces in domains with non-smooth edges. II ⋮ Equations of Maxwell type ⋮ Embedding Theorems for Functional Spaces Associated with a Class of Hermitian Forms ⋮ On Initial Boundary Value Problem for Parabolic Differential Operator with Non-coercive Boundary Conditions

Cites Work

• On iterations of Green type integrals for matrix factorizations of the Laplace operator
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Bases With Double Orthogonality in the Cauchy Problem for Systems With Injective Symbols
• On Iterations of the Green Integrals and their Applications to Elliptic Differential Complexes
• Hölder and L^p estimates for solutions of ∂u = f in strongly pseudoconvex domains
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item