By Irina Mitrea,Marius Mitrea
Many phenomena in engineering and mathematical physics may be modeled by way of boundary worth difficulties for a undeniable elliptic differential operator in a given area. whilst the differential operator less than dialogue is of moment order various instruments can be found for facing such difficulties, together with boundary vital tools, variational tools, harmonic degree suggestions, and strategies according to classical harmonic research. whilst the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending whilst one bargains with a fourth order operator) just a couple of ideas can be effectively applied. within the Seventies Alberto Calderón, one of many founders of the trendy thought of Singular fundamental Operators, endorsed using layer potentials for the therapy of higher-order elliptic boundary worth difficulties. the current monograph represents the 1st systematic remedy in line with this approach.
This examine monograph lays, for the 1st time, the mathematical origin aimed toward fixing boundary worth difficulties for higher-order elliptic operators in non-smooth domain names utilizing the layer capability approach and addresses a complete diversity of issues, facing elliptic boundary price difficulties in non-smooth domain names together with layer potentials, bounce relatives, non-tangential maximal functionality estimates, multi-traces and extensions, boundary price issues of facts in Whitney–Lebesque areas, Whitney–Besov areas, Whitney–Sobolev- established Lebesgue areas, Whitney–Triebel–Lizorkin spaces,Whitney–Sobolev-based Hardy areas, Whitney–BMO and Whitney–VMO spaces.
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Multi-Layer Potentials and Boundary Problems: for Higher-Order Elliptic Systems in Lipschitz Domains (Lecture Notes in Mathematics) by Irina Mitrea,Marius Mitrea