Nečas, Jindřich Sur la régularité des solutions variationnelles des équations elliptiques non-linéaires d’ordre \(2k\) en deux dimensions. (French) Zbl 0171.09401 Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 21, 427-457 (1967). Reviewer: D. Pascali Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 11 Documents MSC: 49J40 Variational inequalities 35J35 Variational methods for higher-order elliptic equations 35J60 Nonlinear elliptic equations 35B65 Smoothness and regularity of solutions to PDEs Keywords:variational calculus × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] S. Agmon , A. Douglis , L. Nirenberg : Estincates near the boundary for solutions of elliptic partial differentiat equations satisfying general boundary conditions I , Comm. Pure Appl. Math. XII ( 1959 ), 623 - 727 . MR 125307 | Zbl 0093.10401 · Zbl 0093.10401 · doi:10.1002/cpa.3160120405 [2] F.E. Browder : Séminaire de mathématiques supérieures , Montreal 1965 . Zbl 0153.17302 · Zbl 0153.17302 [3] F.E. Browder : Variational methods for nonlinear elliptic eigenvalue problems , Bull. Amer. Soc. 71 ( 1965 ), 176 - 183 . Article | MR 179459 | Zbl 0135.15802 · Zbl 0135.15802 · doi:10.1090/S0002-9904-1965-11275-7 [4] E.R. Buley : The differentiability of solutions of certain variational problerrts for multiple integrals , Technical Report 16 ( 1960 ), Univ. Berkeley . [5] E. De Giorgi : Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari , Mem. Accad. Sci. Torino 3 ( 1957 ), 25 - 43 . MR 93649 | Zbl 0084.31901 · Zbl 0084.31901 [6] P. Hartman , G. Stampacchia : On some non-linear elliptic differential functional equations , Acta Math. Uppsala 115 ( 1966 ) 271 - 310 . MR 206537 | Zbl 0142.38102 · Zbl 0142.38102 · doi:10.1007/BF02392210 [7] O.A. Ladyzenskaja , N.N. Uralceva : Linejnyje i kvazilinejnyje uravnenija ellipticeskovo tipa , Izd. Nauka , Moskva 1964 . MR 211073 [8] N.G. Meyers : On Lp cstianates for the gradient of solutions of second order elliptic divergence equations . Ann. Scuola Norm. Sup. Pisa 17 ( 1963 ), 189 - 206 . Numdam | MR 159110 | Zbl 0127.31904 · Zbl 0127.31904 [9] C.B. Morrey : Quelques résultats récents du calcul des variations , Colloque CNRS , Paris 1962 . Zbl 0229.49002 · Zbl 0229.49002 [10] C.B. Morrey : Multiple integrals in the calculus of variations , Springer 1966 . Zbl 0142.38701 · Zbl 0142.38701 [11] C.B. Morrey : Existence and differentiability theorems for the solutions of variational problems for multiple integrals , Bull. Amer. Math. Soc. 46 ( 1940 ), 439 - 458 . Article | MR 2473 | Zbl 0063.04105 | JFM 66.0476.02 · Zbl 0063.04105 · doi:10.1090/S0002-9904-1940-07229-5 [12] J. Nečas : Sur l’existence et le régularité des solutions des équations non-Lïnéaires du type elliptique , Proc. Equadiff II, Bratislava 1966 . [13] J. Necas : Les méthodes directes en théorie des équations elliptiques , Praque 1967 . MR 227584 · Zbl 1225.35003 [14] J. Nečas : Sur la méthode variationnelle pour les équations aux dérivées partielles non-linéaires du type elliptique , CMUC 7 , 3 , ( 1966 ), 301 - 317 . MR 206470 | Zbl 0151.15102 · Zbl 0151.15102 [15] J. Nečas : Sur les domaines du type N , Czechslovak Math. Journ. 12 ( 1962 ), 274 - 287 . Article | Zbl 0106.27001 · Zbl 0106.27001 [16] L. Nirenrerg : Remarks on strongly elliptic partial differential equations , Comm. Pure Appl. Math. 8 ( 1955 ), 648 - 674 . MR 75415 | Zbl 0067.07602 · Zbl 0067.07602 · doi:10.1002/cpa.3160080414 [17] G. Stampacchia : Séminaire de mathéntatiques supérieures , Montréal 1965 . Zbl 0151.15501 · Zbl 0151.15501 [18] M.M. Vajnberg : Variacionnyje metody issledovanija nelinejnych operatorov , Moskva 1956 . [19] A. Zygmund : Trigonometrical series , Cambridge 1959 . · Zbl 0085.05601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.