Behaviour in the limit, AS p → ∞, of minimizers of functionals involving p-Dirichlet integrals

SIAM Journal on Mathematical Analysis

Volumn 27, Issue 2, 1996, Pages 341-360

  Janfalk, Ulf ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Capacitary function; Convex duality; Green function; p Dirichlet integral; P harmonic; Ridge; Variational solution

Indexed keywords

EID: 0001179653     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141093252619     Document Type: Article

References (19)

1. R. A. ADAMS, Sobolev Spaces, Academic Press, London, New York, 1975.
2. G. ARONSSON, Extension of functions satisfying Lipschitz conditions, Ark. Mat., 6 (1967), pp. 551-561.
3. yy = 0, Ark. Mat., 7 (1968), pp. 395-425.
4. _, Representation of a p-harmonic function near a critical point in the plane, Manuscripta Math., 66 (1989), pp. 73-95.
5. p = f and related extremal problems, Rend. Sem. Mat. Univ. Politec. Torino, (1989), pp. 15-68.
6. H. BUSEMANN, The Geometry of Geodesics, Academic Press, New York, 1955.
7. W. D. EVANS AND D. J. HARRIS, Sobolev embeddings for generalized ridged domains, Proc. London Math. Soc., 54 (1987), pp. 141-175.
8. I. EKELAND AND R. TEMAM, Convex Analysis and Variational Problems, North-Holland, Amsterdam, Oxford, 1976.
9. J. HEINONEN, T. KILPELÄINEN, AND O. MARTIO, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, Oxford, 1993.
10. I. HOLOPAINEN, Nonlinear Potential Theory and Quasiregular Mappings on Riemannian Manifolds, Ann. Acad. Sci. Fenn., Ser. A I Math. Dissertationes, 74, 1990.
11. R. JENSEN, Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient, Arch. Rational Mech. Anal., 123 (1993), pp. 51-74.
12. B. KAWOHL, On a family of torsional creep problems, J. Reine Angew. Math., 410 (1990), pp. 1-22
13. J. LEWIS, Capacitary functions in convex rings, Arch. Rational Mech. Anal., 66 (1977), pp. 201-224.
14. V. G. MAZ'YA, Sobolev Spaces, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985.
15. _, On the continuity at a boundary point of solutions of quasi-linear elliptic equations, Vestnik Leningrad Univ. Math., 3 (1976), pp. 225-242 (in English); Vestnik Leningradskogo Universiteta, 25 (1970), pp. 42-55 (in Russian).
16. _, On the continuity at a boundary point of solutions of quasi-linear elliptic equations, Vestnik Leningrad Univ. Math., 3 (1976), pp. 225-242 (in English); Vestnik Leningradskogo Universiteta, 25 (1970), pp. 42-55 (in Russian).
17. J. SERRIN, Applications of nonlinear partial differential equations in mathematical physics, Proc. Sympos. Appl. Math, XVII (1965), pp. 68-88.
18. P. TOLKSDORF, Invariance properties and special structures near conical boundary points, Lecture Notes in Mathematics 1121, Springer-Verlag, Berlin, Heidelberg, New York, 1985, pp. 308-318.
19. W. P. ZIEMER, Weakly Differentiate Functions, Springer-Verlag, Berlin, Heidelberg, New York, 1989.