Titlebook: Singular Integral Operators, Quantitative Flatness, and Boundary Problems; Juan José Marín,José María Martell,Marius Mitrea Book 2022 The

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Singular Integrals and Boundary Problems in Weighted Banach Function Spaces, for boundary problems for second-order weakly elliptic systems formulated in sufficiently flat Ahlfors regular domains and with boundary data in weighted Banach function spaces (aka, K?the function spaces). In the first part we develop the theory of boundary layer potentials and boundary value prob

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,Calderón–Zygmund Theory for Boundary Layers in UR Domains,specialized properties requires placing additional demands on the coefficient tensor .. We are especially interested to identify, in this library of coefficient tensors, those “distinguished coefficient tensors” giving rise to double layer potential operators which vanish identically when considered in half-spaces.

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Singular Integrals and Boundary Problems in Weighted Banach Function Spaces,lems in such a general functional analytic setting then, in the last part of this chapter, we specialize this discussion to the case of rearrangement invariant Banach function spaces (RIBFS for short), including Orlicz spaces, Zygmund space, Lorentz spaces, and their weighted versions.

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Book 2022iptic boundary value problems with boundary data in a multitude of function spaces.?Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic

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0743-1643 to establish a bridge between analysis and geometry.IncludeThis monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces.?Many s

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