Displaying similar documents to “Boundary value problems and duality between Lp Dirichlet and regularity problems for second order parabolic systems in non-cylindrical domains.”

A boundary integral equation for Calderón's inverse conductivity problem.

Kari Astala, Lassi Päivärinta (2006)

Collectanea Mathematica

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Towards a constructive method to determine an L-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L-conductivity problem can be determined in a stable manner at the boundary and outside of the body.

On the Moser-Onofri and Prékopa-Leindler inequalities.

Alessandro Ghigi (2005)

Collectanea Mathematica

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Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that 1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0 for any funcion φ ∈ C∞(S2).

A generalization of the Nikodym boundedness theorem.

Christopher Stuart (2007)

Collectanea Mathematica

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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.

Rough Marcinkiewicz integral operators on product spaces.

Hussein M. Al-Qassem (2005)

Collectanea Mathematica

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In this paper, we study the Marcinkiewicz integral operators M on the product space R x R. We prove that M is bounded on L(R x R) (1< p < ∞) provided that h is a bounded radial function and Ω is a function in certain block space B (S x S) for some q > 1. We also establish the optimality of our condition in the sense that the space B (S x S) cannot be replaced by B (S x S) for any −1 < r < 0. Our results...

Painlevé's problem and analytic capacity.

Xavier Tolsa (2006)

Collectanea Mathematica

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In this paper we survey some recent results in connection with the so called Painlevé's problem and the semiadditivity of analytic capacity γ. In particular, we give the detailed proof of the semiadditivity of the capacity γ, and we show almost completely all the arguments for the proof of the comparability between γ and γ.