On the role of energy convexity in the web function approximation

Nonlinear Differential Equations and Applications

Volumn 12, Issue 1, 2005, Pages 93-109

  Crasta, Graziano ^a   Fragalà, Ilaria ^b   Gazzola, Filippo ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Convexity; Minimization; Planar shapes; Web functions

Indexed keywords

EID: 21644464060     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00030-004-2024-2     Document Type: Article

References (16)

1. C. BANDLE, Isoperimetric inequalities and applications, Pitman 1980
2. p = f and related extremal problems, Rend. Sem. Mat. Univ. Pol. Torino, Some topics in nonlinear PDE's, Special issue (1989), 15-61.
3. F. BROCK, J. PRAJAPAT, Some new symmetry results for elliptic problems on the sphere and in Euclidean space, Rend. Circ. Mat. Palermo 49 (2000), 445-162.
4. D. BUCUR, G. BUTTAZZO, Variational Methods in some Shape Optimization Problems, Lecture Notes of courses at Dipartimento di Matematica Università di Pisa and Scuola Normale Superiore di Pisa, Series "Appunti di Corsi della Scuola Normale Superiore" (2002).
5. A. CELLINA, Minimising a functional depending on ∇u and on u, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), 339-352.
6. G. CRASTA, Variational problems for a class of functionals on convex domains, J. Differential Equations 178 (2002), 608-629.
7. G. CRASTA, I. FRAGALÀ, F. GAZZOLA, A sharp upper bound for the torsional rigidity of rods by means of web functions, Arch. Rational Mech. Anal. 164 (2002), 189-211.
8. G. CRASTA, F. GAZZOLA, Some estimates of the minimizing properties of web functions, Calc. Var. Partial Differential Equations 15 (2002), 45-66.
9. G. CRASTA, F. GAZZOLA, Web functions: survey of results and perspectives, Rend. Ist. Mat. Univ. Trieste 33 (2001), 313-326.
10. L. DAMASCELLI, F. PACELLA, Monotonicity and symmetry results for p-Laplace equations and applications, Adv. Differential Equations 5 (2000), 1179-1200.
11. 1,α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 8 (1983), 827-850.
12. F. GAZZOLA, Existence of minima for nonconvex functionals in spaces of functions depending on the distance from the boundary, Arch. Rational Mech. Anal. 150 (1999), 57-76.
13. B. KAWOHL, On a family of torsional creep problems, J. Reine Angew. Math. 410 (1990), 1-22.
14. S. SAKAGUCHI, Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 14(4) (1987), 389-402.
15. R. SCHNEIDER, Convex bodies: the Brunn-Minkowski theory, Cambridge Univ. Press, 1993.
16. P. TOLKSDORF, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 126-150.