Trace imbeddings for $T$-sets and application to Neumann-Dirichlet problems with measures included in the boundary data

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1. [A] Adams ( R.A.) .— Sobolev spaces, New York, Academic Press1980. 
2. [At] Atik ( Y.) .— T-ensembles locaux et problèmes quasi linéaires dégénérés à donnée mesure sur un ouvert quelconque, P.H.D. Thesis at Univ. Poitiers, 1993. 
3. [BBGGVP] Benilan ( P.), Boccardo ( L.), Gallouët ( T.), Gariepy ( R.) and Pierre ( M.) .— An L1-theory of existence and uniqueness of solution of non linear elliptic equation, Ann. Scuola Norm. Sup. di Pisa, serie IV, 22 (1995), pp. 241-273. Zbl0866.35037MR1354907
4. [BCP] Benilan ( P.), Crandall ( M.G.) and Pierre ( M.) .— Solution of the porous medium equation in Rn under optimal conditions, Indiana Univ. Math. J.33, n° 1 (1984). Zbl0552.35045MR726106
5. [BDG] Boccardo ( L.), Diaz ( J.-L.), Giachetti ( D.) and Murat ( F.) .— Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms, J. Diff. Equ.186, n° 2 (1993), pp. 215-237. Zbl0803.35046MR1251852
6. [BG] Boccardo ( L.) and Gallouet ( T.) .— Nonlinear elliptic and parabolic equations involving measures as data, J. Funct. Anal.87 (1989), pp. 149-169. Zbl0707.35060MR1025884
7. [BGM] Boccardo ( L.), Giachetti ( D.) and Murat ( F.) . — Renormalizedsolutions of non linear elliptic problems. Methods of real analysis and p.d.e., an international Workshop, Capri 17-20 ( sept.1990). 
8. [BGV] Boccardo ( L.), Gallouet ( T.) and Vasquez ( J.L.), .— Nonlinear elliptic equations in Rn without growth restrictions on the data, to appear in J.D.E. Zbl0810.35021MR1025884
9. [BS] Brezis ( H.) and Strauss ( W.) .— Semilinear elliptic equations in L1, Jour. Math. Soc. Japan, 25 (1973), pp. 565-590. Zbl0278.35041MR336050
10. [GM] Gmira ( A.) and Véron ( L.) .— Boundary singularities of solutions of some nonlinear elliptic equations, Duke Math. J.64 (1991), pp. 271-324. Zbl0766.35015MR1136377
11. [Lia] Liang ( J.) .— Weakly-coercive quasilinear elliptic equations with inhomogeneous measure data, Progress in partial differential equation "Proceedings of the Pont-à-Mousson Conference" (1991), Pitman; Res. Notes Math.266, Longman, Harlow1992. Zbl0821.35045MR1194227
12. [L] Lions ( P.-L.) .— Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1968. Zbl0189.40603
13. [LL] Leray ( J.) and Lions ( J.-L.) .— Quelques résultats de Visik sur les problèmes elliptiques non linéaires par les méthodes de Minty—Browder, Bull. Soc. Math. France, 93 (1965), pp. 97-107. Zbl0132.10502MR194733
14. [LM] Lions ( P.-L.) and Murat ( F.) .— Sur les solutions renormalisées d'équations elliptiques non linéaires, Manuscript for C.R.A.S. (juin 1992). 
15. [Ra1] Rakotoson ( J.-M.) .— Quasilinear elliptic problems with measures as data, Diff. Int. Equ.4 (1991), pp. 449-457. Zbl0834.35056MR1097910
16. [Ra2] Rakotoson ( J.-M.) . — Resolution of the critical case forproblems with L1-data, Asymptotic Analysis6 (1993), pp. 285-293. Zbl0793.35042MR1201197
17. [Ra3] Rakotoson ( J.-M.) .— Generalized solution in a new type of sets for solving problems with measures as data, Diff. Int. Equ. Vol 6, n° 1 (1993), pp. 27-36. Zbl0780.35047MR1190163
18. [Ra4] Rakotoson ( J.-M.) .- A compactness lemma for elliptic problems with measures as data, Applied Math. Letters4 (1991), pp. 35-36. Zbl0734.35147MR1101870
19. [Ra5] Rakotoson ( J.-M.) .— Compactness and doubly degenerate quasilinear problems with measures as data, Preprint 9107, Bloomington. 
20. [Ra6] Rakotoson ( J.-M.) .— Uniqueness of renormalized solutions in a T-set for L1-data problem and the link between various formulations, in Indiana Univ. Math. J.43, n° 2 (1994), pp. 685-702. Zbl0805.35035MR1291535
21. [RT] Rakotoson ( J.-M.) and Temam ( R.) .— A coarea formula with applications to monotone rearrangement and to regularity, Arch. Rational Mech. Anal.109 (1990), pp. 213-238. Zbl0735.49039MR1025171
22. [Se] Serrin ( J.) .— Pathological solutions of elliptic differential equations, Ann. Sc. Scuola Norm. Sup. di Pisa serie 3, vol. XVIII, 3 (1964). Zbl0142.37601MR170094
23. [X] Xu ( X.) .- A p-Laplacian problem in L1 with nonlinear boundary conditions, Comm. Partial Diff. Equ.19 (vol. 1-2) 1994, pp. 143-179. Zbl0858.35147MR1257001