Analyticity of layer potentials and <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> solvability of boundary value problems for divergence form elliptic equations with complex <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>L</mml:mi><mml:mo>?</mml:mo></mml:msup></mml:math> coefficients, Advances in Mathematics, vol.226, issue.5, pp.4533-4606, 2011. ,
DOI : 10.1016/j.aim.2010.12.014
Non negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa, vol.22, issue.3, pp.607-694, 1968. ,
On non-autonomous maximal regularity for elliptic operators in divergence form, Archiv der Mathematik, vol.237, issue.3, pp.271-284, 2016. ,
DOI : 10.1002/1522-2616(200204)237:1<125::AID-MANA125>3.0.CO;2-3
URL : https://hal.archives-ouvertes.fr/hal-01278498
L 2 well-posedness of boundary value problems and the Kato square root problem for parabolic systems with measurable coefficients Available at https://arxiv.org/abs, pp.12-14, 1607. ,
Extrapolation of Carleson measures and the analyticity of Kato's square-root operators, Acta Mathematica, vol.187, issue.2, pp.161-190, 2001. ,
DOI : 10.1007/BF02392615
Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients, Calculus of Variations and Partial Differential Equations, vol.57, issue.2, pp.124-125, 2016. ,
DOI : 10.5565/PUBLMAT_57213_08
Weighted norm inequalities for maximal function and singular integrals, Studia Math, vol.51, pp.241-250, 1974. ,
On estimates of harmonic measure, Arch Rational Mech, Anal, vol.65, pp.275-288, 1977. ,
BMO solvability and the A? condition for second order parabolic operators Available at https://arviv.org/abs, p.5, 1510. ,
On Kato's conjecture and mixed boundary conditions, 2015. ,
DOI : 10.1016/j.jfa.2014.06.003
URL : http://arxiv.org/abs/1311.0302
Behavior near the boundary of positive solutions of second order parabolic equations, The Journal of Fourier Analysis and Applications, vol.128, issue.S1, pp.871-882, 1997. ,
DOI : 10.1007/BF02656492
Behavior near the boundary of positive solutions of second order parabolic equations, The Journal of Fourier Analysis and Applications, vol.128, issue.S1, pp.4947-4961, 1999. ,
DOI : 10.1007/BF02656492
Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders, Transactions of the American Mathematical Society, vol.279, issue.2, pp.279-635, 1983. ,
DOI : 10.1090/S0002-9947-1983-0709573-7
Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators, Journal of the American Mathematical Society, vol.28, issue.2, pp.483-529, 2005. ,
DOI : 10.1090/S0894-0347-2014-00805-5
L 2 Solvability and Representation by Caloric Layer Potentials in Time- Varying Domains, The Annals of Mathematics, vol.144, issue.2 ,
DOI : 10.2307/2118595
The Dirichlet problem for parabolic operators with singular drift terms, Memoirs of the American Mathematical Society, vol.151, issue.719, 2001. ,
DOI : 10.1090/memo/0719
The ${L}^p$ Neumann problem for the heat equation in non-cylindrical domains, Journ??es ??quations aux d??riv??es partielles, vol.220, pp.1-54, 2005. ,
DOI : 10.5802/jedp.535
The Dirichlet Problem in Non-Smooth Domains, The Annals of Mathematics, vol.113, issue.2, pp.367-382, 1981. ,
DOI : 10.2307/2006988
Harmonic analysis techniques for second order elliptic boundary value problems. CBMS Regional conference series in mathematics 83, 1994. ,
DOI : 10.1090/cbms/083
Square Functions and the $$A_\infty $$ A ??? Property of Elliptic Measures, The Journal of Geometric Analysis, vol.17, issue.4, pp.2383-2410, 2016. ,
DOI : 10.1007/s00208-010-0586-3
The method of layer potentials for the heat equation in time-varying domains, Memoirs of the American Mathematical Society, vol.114, issue.545, p.1, 1995. ,
DOI : 10.1090/memo/0545
Second order parabolic differential equations, p.15, 1996. ,
DOI : 10.1142/3302
Operators which have an H ? functional calculus, Miniconference on operator theory and partial differential equations, pp.210-231, 1986. ,
The Dirichlet problem for second order parabolic operators, Indiana University Mathematics Journal, vol.46, issue.1, pp.183-245, 1997. ,
DOI : 10.1512/iumj.1997.46.1277
Square function estimates and the Kato problem for second order parabolic operators in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>, Advances in Mathematics, vol.293, issue.1 6, pp.1-36, 2016. ,
DOI : 10.1016/j.aim.2016.02.006
L2 Solvability of boundary value problems for divergence form parabolic equations with complex coefficients, Journal of Differential Equations, vol.262, issue.3, pp.2808-2939, 2016. ,
DOI : 10.1016/j.jde.2016.11.011
Absolute continuity of parabolic measure and area integral estimates in non-cylindrical domains, Indiana University Mathematics Journal, vol.52, issue.2, pp.477-525, 2003. ,
DOI : 10.1512/iumj.2003.52.2210