Weighted a priori estimates for the poisson equation
Let Ω be a bounded domain in (ℝn with ∂Ω ∈ C2 and let u be a solution of the classical Poisson problem in Ω; i.e., (Equation Presented) where f ∈ Lω p, (Ω) and ω is a weight in Ap. The main goal of this paper is to prove the following a priori estimate (Equation Presented) and to give some applicati...
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2008
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| LEADER | 05777caa a22004817a 4500 | ||
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| 003 | AR-BaUEN | ||
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| 008 | 190411s2008 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-62649154758 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Durán, R.G. | |
| 245 | 1 | 0 | |a Weighted a priori estimates for the poisson equation |
| 260 | |c 2008 | ||
| 270 | 1 | 0 | |m Durán, R.G.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina; email: rduran@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a ACOSTA, G., DURÁN, R.G., LOMBARDI, A.L., (2006) Weighted Poincaré and Korn inequalities for Hölder α domains, 29, pp. 387-400. , http://dx.doi.org/10.1002/mma.680, Math. Methods Appl. Sci, MR 2198138 2006i:26020 | ||
| 504 | |a S. AGMON, Lectures on Elliptic Boundary Value Problems, Mathematical Studies, 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand. MR 0178246 (31 #2504); AGMON, S., DOUGLIS, A., NIRENBERG, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I (1959) Comm. Pure Appl. Math, 12, pp. 623-727. , MR 0125307 23 #A2610 | ||
| 504 | |a BUCKLEY, S.M., KOSKELA, P., New Poincaré inequalities from old (1998) Ann. Acad. Sci. Fenn. Math, 23, pp. 251-260. , MR 1601883 99a:46057 | ||
| 504 | |a CALDERON, A.P., ZYGMUND, A., On the existence of certain singular integrals (1952) Acta Math, 88, pp. 85-139. , http://dx.doi.org/10.1007/BF02392130.MR0052553, 14,637f | ||
| 504 | |a A. DALL'ACQUA and G. SWEERS, Estimates for Green function and Poisson kernels of higher-order Dirichlet boundary value problems, J. Differential Equations 205 (2004), 466-487, http://dx.doi.org/10.1016/j-jde.2004.06.004. MR 2092867 (2005i:35065); GRÜTER, M.L., WIDMAN, K.-O., The Green function for uniformly elliptic equations (1982) Manuscripta Math, 37, pp. 303-342. , http://dx.doi.org/10.1007/BF01166225.MR657523, 83h:35033 | ||
| 504 | |a J.J. MANFREDI and E. VILLAMOR, Traces of monotone functions in weighted Sobolev spaces, Illinois J. Math. 45 (2001), 403-422. MR 1878611 (2003g:31005); MUCKENHOUPT, B., Weighted norm inequalities for the Hardy maximal function (1972) Trans. Amer. Math. Soc, 165, pp. 207-226. , http://dx.doi.org/10.2307/1995882.MR0293384, 45 #2461 | ||
| 504 | |a NEČAS, J., (1967) Les méthodes directes en théorie des équations elliptiques, , Masson et Cie, Éditeurs, Paris, MR 0227584 37 #3168, French | ||
| 504 | |a E.M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095 (44 #7280); -, Harmonic Analysis: Rreal-variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, 43, Princeton University Press, Princeton, NJ, 1993, ISBN 0-691-03216-5, With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192 (95c:42002); P. SOUPLET, A survey on Lδ p spaces and their applications to nonlinear elliptic and parabolic problems, Nonlinear Partial Differential Equations and Their Applications, GAKUTO Internat. Ser. Math. Sci. Appl., 20, Gakkōtosho, Tokyo, 2004, pp. 464-479. MR 2087491; WIDMAN, K.-O., (1967) Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, 21, pp. 17-37. , Math. Scand, MR 0239264 39 #621 | ||
| 504 | |a HARJULEHTO, P., Traces and Sobolev extension domains (2006) Proc. Amer. Math. Soc, 134, pp. 2373-2382. , http://dx.doi.org/10.1090/S0002-9939-06-08228-1, electronic, MR 2213711 2007a:46032 | ||
| 504 | |a ZIEMER, W.P., Weakly Differentiate Functions (1989) Graduate Texts in Mathematics, 120. , Springer-Verlag, New York, ISBN 0-387-97017-7, Sobolev spaces and functions of bounded variation. MR 1014685 91e:46046 | ||
| 520 | 3 | |a Let Ω be a bounded domain in (ℝn with ∂Ω ∈ C2 and let u be a solution of the classical Poisson problem in Ω; i.e., (Equation Presented) where f ∈ Lω p, (Ω) and ω is a weight in Ap. The main goal of this paper is to prove the following a priori estimate (Equation Presented) and to give some applications for weights given by powers of the distance to the boundary. |l eng | |
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de la Plata, 1900 La Plata (Buenos Aires), Argentina | ||
| 690 | 1 | 0 | |a CALDERON-ZYGMUND THEORY |
| 690 | 1 | 0 | |a GREEN FUNCTION |
| 690 | 1 | 0 | |a POISSON EQUATION |
| 690 | 1 | 0 | |a WEIGHTED SOBOLEV SPACES |
| 700 | 1 | |a Sanmartino, M. | |
| 700 | 1 | |a Toschi, M. | |
| 773 | 0 | |d 2008 |g v. 57 |h pp. 3463-3478 |k n. 7 |p Indiana Univ. Math. J. |x 00222518 |w (AR-BaUEN)CENRE-140 |t Indiana University Mathematics Journal | |
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| 856 | 4 | 0 | |u https://doi.org/10.1512/iumj.2008.57.3427 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00222518_v57_n7_p3463_Duran |y Handle |
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