×

zbMATH — the first resource for mathematics

A regularity condition at the boundary for solutions of quasilinear elliptic equations. (English) Zbl 0389.35023

MSC:
35J60 Nonlinear elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Adams, D., & N. Meyers, Thinness and Wiener Criteria for non-linear potentials, Indiana U. Math. J., 22, 169-197 (1972). · Zbl 0244.31012
[2] Beiras Da Veiga, H., Punti regolari per una classe di operatori ellittici non lineari, Ricerche di Mat. 21 (1972) · Zbl 0245.35036
[3] Bagby, T., Quasitopologies and rational approximation, J. Func. Anal., 10, 259-268 (1972). · Zbl 0266.30024
[4] Beiras Da Veiga, H., & F. Conti, Equazoni ellittiche non lineari con ostacoli sottili, Applicasions allo studio dei punti regolari, Ann. Scuola Normale Sup. Pisa, 26, 533-562 (1972). · Zbl 0259.35034
[5] DeGiorgi, E., Sulla differenziabilità e l’analyticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino 3a, (3), 25-43 (1957).
[6] Federer, H., & W. Ziemer, The Lebesgue set of a function whose distribution derivatives are p-th power integrable, Ind. U. Math. J., 22, 139-158 (1972). · Zbl 0238.28015
[7] Gariepy, R., & W. Ziemer, Behavior at the boundary of solutions of quasilinear elliptic equations, Arch. Rational Mech. Anal., 56, 372-384 (1974). · Zbl 0297.35032
[8] Gariepy, R., & W. Ziemer, A gradient estimate at the boundary for solutions of quasilinear elliptic equations, Bull. Amer. Math. Soc., 82, 629-631 (1976). · Zbl 0336.35045
[9] Hedberg, L., Non-linear potentials and approximation in the mean by analytic functions, Math. Z., 129, 299-319 (1972). · Zbl 0243.31014
[10] Krol’, I.N., & V.G. Maz’ja, On the absence of continuity and Hölder continuity of solutions of quasilinear elliptic equations near a nonregular point, Trans. Moscow Math. Soc., 26, 73-93 (1972). · Zbl 0281.35013
[11] Littman, W., G. Stampacchia, & H. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Normale Sup. Pisa, 17, 43-77 (1963). · Zbl 0116.30302
[12] Ladyzhenskaya, O.A., & Ural’tseva, Linear and quasilinear elliptic equations, New York: Academic Press 1968. · Zbl 0164.13002
[13] Maz’ja, V.G., On the continuity at a boundary point of the solution of quasi-linear elliptic, equations (Russian), Vestnik Leningrad Univ., 25, 42-55 (1970).
[14] Meyers, N., & Elcrat, Alan, Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions, Duke Math. J., 42, 121-136 (1975). · Zbl 0347.35039
[15] Meyers, N., Continuity properties of potentials, Duke Math. J., 42, 157-165 (1975). · Zbl 0334.31004
[16] Moser, J., A new proof of DeGiorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm. Pure and Appl. Math., 13, 457-468 (1960). · Zbl 0111.09301
[17] Moser, J., On Harnack’s theorem for elliptic differential equations, Comm. Pure and Appl. Math., 14, 577-591 (1961). · Zbl 0111.09302
[18] Morrey, C.B., Multiple integrals in the calculus of variations, Springer-Verlag, New York, 1966. · Zbl 0142.38701
[19] Serrin, J., Local behavior of solutions of quasilinear equations, Acta Math., III, 302-347 (1964). · Zbl 0128.09101
[20] Serrin, J., On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc., 101, 139-167 (1961). · Zbl 0102.04601
[21] Stampacchia, G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15, 189-258 (1965). · Zbl 0151.15401
[22] Trudinger, N., On Harnack type inequalities and their application to quasilinear equations, Comm. Pure and Appl. Math, 20, 721-747 (1967). · Zbl 0153.42703
[23] Voinov, Je. N., s-capacity in the proof of Hölder continuity of weak solutions to quasilinear near the boundary, Pet. Rar. Ped. Inst. Ueh. Zap., 20, 3-9 (1967).
[24] Wiener, N., The Dirichlet problem, J. Math. and Phys. 3, 127-146 (1924). · JFM 51.0361.01
[25] Wiener, N., Certain notions in potential theory, J. Math. and Phys. 3, 24-51 (1924). · JFM 50.0646.03
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.