Sharp Conditions for Korn Inequalities in Orlicz Spaces
Tóm tắt
Từ khóa
Tài liệu tham khảo
Adams R.A.: Sobolev Spaces. Academic Press, New York (1975)
Acerbi A., Mingione G.: Regularity results for stationary electro-rheological fluids. Arch. Rat. Mech. Anal. 164, 213–259 (2002)
Breit, D., Diening, L., Fuchs, M.: Existence results for stationary flows of Prandtl-Eyring fluids in 2D by means of solenoidal Lipschitz truncation. OxPDE Technical Report 11/20, University of Oxford
Breit, D., Fuchs, M.: The nonlinear Stokes problem with general potentials having superquadratic growth. J. Math. Fluid Mech. 13, 371–385 (2011)
Conti S., Faraco D., Maggi F.: A new approach to counterexamples to L1 estimates: Korn’s inequality, geometric rigidity, and regularity for gradients of separately convex functions. Arch. Rat. Mech. Anal. 175, 287–300 (2005)
Cruz-Uribe, D., Martell, J.M., Pérez, C.: Extensions of Rubio de Francia’s extrapolation theorem. Collect. Math. (Vol. Extra), 195–231 (2006)
Duvaut G., Lions J.L.: Inequalities in Mechanics and Physics. Springer Grundlehren, vol. 219. Springer, Berlin (1976)
Diening L., Růžička M.: Calderon–Zygmund operators on generalized Lebesgue spaces Lpx and problems related to fluid dynamics. J. Reine Angew. Math. 563, 197–220 (2003)
Diening, L., Růžička, M., Schumacher, K.: A decomposition technique for John domains. Ann. Acad. Sci. Fenn. Math. 35(1), 87–114 (2010). http://dx.doi.org/10.5186/aasfm.2010.3506
Èidus D.M.: On a mixed problem of the theory of elasticity. Dokl. Akad. Nauk SSSR 76, 181–184 (1951)
Eyring H.J.: Viscosity, plasticity, and diffusion as example of absolute reaction rates. J. Chem. Phys. 4, 283–291 (1936)
Friedrichs K.: On the boundary value problems of the theory of elasticity and Korn’s inequality. Ann. Math. 48(2), 441–471 (1947)
Frehse, J., Seregin, G.: Regularity of solutions to variational problems of the deformation theory of plasticity with logarithmic hardening. In: Proceedings of St. Petersburg Mathematical Soceity, vol. 5, pp. 184–222/ English translation: Am. Math. Soc. Transl. II, vol. 193, pp. 127–152 (1998/1999)
Fuchs M.: On stationary incompressible Norton fluids and some extensions of Korn’s inequality. Zeitschr. Anal. Anwendungen 13(2), 191–197 (1994)
Fuchs, M., Seregin, G.: Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids. In: Lecture Notes in Mathematics, vol. 1749. Springer, Berlin (2000)
Gobert J.: Une inéquation fondamentale de la théorie de l’élasticité. Bull. Soc. Roy. Sci. Liege 3-4, 182–191 (1962)
Jia H., Li D., Whang L.: Regularity theory in Orlicz spaces for elliptic equations in Reifenberg domains. J. Math. Anal. Appl. 334, 804–817 (2007)
Kirchheim B., Müller S., Svérak V.: Studying nonlinear pde by geometry in matrix space. In: Hildebrandt, S., Karcher, H. (eds) Geometriy Analysis and Nonlinear Partial Differential Equations, pp. 347–395. Springer, Berlin (2003)
de Leeuw K., Mirkil H.: A priori estimates for differential operators in L ∞ norm. Ill. J. Math. 8, 112–124 (1964)
Müller, S.: Variational models for microstructure and phase transitions. In: Bethuel, F. (ed.) Calculus of variations and geometric evolution problems. Springer Lecture Notes in Math, vol. 1713. Springer, Berlin, pp. 85–210 (1999)
Mihlin S.G.: The Problem of the Minimum of a Quadratic Functional. GITTL, Moscow (1952)
Mosolov P.P., Mjasnikov V.P.: On the correctness of boundary value problems in the mechanics of continuous media. Math. USSR Sbornik 17(2), 257–267 (1972)
Müller S., Svérak V.: Convex integration for Lipschitz mappings and counterexamples to regularity. Ann. Math. 157, 715–742 (2003)
Málek J., Necaˇs J., Rokyta M., Růžička M.: Weak and Measure Valued Solutions to Evolutionary PDEs. Chapman & Hall, London (1996)
Nečas, J.: Sur les normes équivalentes dans $${W_k^p(\Omega)}$$ et sur la coecivité des formes formellement positives. In: Séminaire Equations aus Dérivées Partielles, Les Presses de l’Université de Montréal, pp. 102–128 (1966)
Ornstein D.: A non-inequality for differential operators in the L 1 norm. Arch. Rational Mech. Anal. 11, 40–49 (1964)
Růžička, M.: Electrorheological Fluids: Modeling and Mathematical Theory. In: Lecture Notes in Mathematics, vol. 1748. Springer (2000)
Temam R.: Mathematical Problems in Plasticity. Gauthier Villars, Paris (1985)
Zeidler E.: Nonlinear Functional Analysis II/B-Nonlinear Monotone Operators. Springer, Berlin (1987)