Geodesic
Characterization of the interior regularity for parabolic systems with discontinuous coefficients
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 2, pp. 125-132.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We deal in this Note with linear parabolic (in sense of Petrovskij) systems of order $2b$ with discontinuous principal coefficients belonging to $VMO \bigcap L^{\infty}$. By means of a priori estimates in Sobolev-Morrey spaces we give a precise characterization of the Morrey, BMO and Hölder regularity of the solutions and their derivatives up to order $2b-1$.
In questa Nota si studiano dei sistemi lineari parabolici (in senso di Petrovskij) di ordine $2b$ con coefficienti principali appartenenti a $VMO \bigcap L^{\infty}$. Per mezzo di stime a priori negli spazi di Sobolev-Morrey si propone una caratterizzazione precisa della regolaritaÁ (Morrey, BMO e Hölder) all'interno delle soluzioni e le loro derivate fino all'ordine $2b-1$. 
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Palagachev, Dian K.; Softova, Lubomira G. Characterization of the interior regularity for parabolic systems with discontinuous coefficients. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 2, pp. 125-132. http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_2_a4/

[1] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math., vol. 12, 1959, 623-727. | MR | Zbl

[2] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Comm. Pure Appl. Math., vol. 17, 1964, 35-92. | MR | Zbl

[3] S. Campanato, Proprietà di Hölderianità di alcune classi di funzioni. Ann. Scuola Norm. Sup. Pisa, vol. 17, 1963, 175-188. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[4] F. Chiarenza - M. Franciosi - M. Frasca, $L^{p}$-Estimates for linear elliptic systems with discontinuous coefficients. Rend. Mat. Acc. Lincei, s. 9, vol. 5, 1994, 27-32. | fulltext bdim | fulltext EuDML | fulltext mini-dml | MR | Zbl

[5] G. Da Prato, Spazi $\mathcal L^{p,\theta}(\Omega,\delta)$ e loro proprietà. Ann. Mat. Pura Appl., vol. 69, 1965, 383-392. | MR | Zbl

[6] A. Douglis - L. Nirenberg, Interior estimates for elliptic systems of partial differential equations. Comm. Pure Appl. Math., vol. 8, 1955, 503-538. | MR | Zbl

[7] S.D. Ejdel'Man, Parabolic Equations. In: YU.V. EGOROV - M.A. SHUBIN (eds.), Partial Differential Equations VI: Elliptic and Parabolic Operators. Encycl. Math. Sci., vol. 63, Springer-Verlag, Berlin 1994, 203-316. | DOI | MR | Zbl

[8] E.B. Fabes - N. Rivière, Singular integrals with mixed homogeneity. Studia Math., vol. 27, 1966, 19-38. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[9] A. Friedman, Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, N.J., 1964. | MR | Zbl

[10] F. John - L. Nirenberg, On functions of bounded mean oscillation. Comm. Pure Appl. Math., vol. 14, 1961, 415-426. | MR | Zbl

[11] M. Kronz, Some function spaces on spaces of homogeneous type. Manuscr. Math., vol. 106, 2001, 219-248. | DOI | MR | Zbl

[12] A. Maugeri - D.K. Palagachev - L.G. Softova, Elliptic and Parabolic Equations with Discontinuous Coefficients. Wiley-VCH, Berlin 2000. | DOI | MR | Zbl

[13] D.K. Palagachev - L.G. Softova, Singular integral operators, Morrey spaces and fine regularity of solutions to PDE's. Potential Anal., vol. 20, 2004, 237-263. | DOI | MR | Zbl

[14] D. Sarason, Functions of vanishing mean oscillation. Trans. Amer. Math. Soc., vol. 207, 1975, 391-405. | MR | Zbl

[15] V.A. Solonnikov, On the boundary value problems for linear parabolic systems of differential equations of general form. Proc. Steklov Inst. Math., vol. 83, 1965 (in Russian); English translation: O.A. LADYZHENSKAYA (ed.), Boundary Value Problems of Mathematical Physics III. Amer. Math. Soc., Providence, R.I., 1967. | Zbl