J. Frehse, On the Regularity of the Solution of a Second Order Variational Inequality, Boll. Un. Mat. Ital. B (7) 6 (4), (1972), 312-315.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in L with gradient in L The rst term in the energy (1.2) is a kind of elastic energy and the second term is a kind of gravity energy for a heavy membrane. The well posedness and good properties of the obstacle problem are guaranteed by the following result for 0: Theorem 1.1 (J. Frehse [18], C Regularity of the Minimizer) There exists a unique solution u minimizing energy (1.2) on the convex set K de ned in (1.3) Moreover this solution satis es u = 1 on fu 0g ) 1.4) The coincidence set is fu = 0g and the free boundary is fu = 0g. 1.3 Main results Let us ....

J. Frehse, On the Regularity of the Solution of a Second Order Variational Inequality, Boll. Un. Mat. Ital. B (7) 6 (4), (1972), 312-315.

....2( with gradient in L 2( 7 The rst term in the energy (1.2) is a kind of elastic energy and the second term is a kind of gravity energy for a heavy membrane. The well posedness and good properties of the obstacle problem are garanteed by the following result for 0: Theorem 1.1 (J. Frehse [18], C 1;1 Regularity of the Minimizer) There exists a unique solution u minimizing energy (1.2) on the convex set K de ned in (1.3) Moreover this solution satis es 8 : u = 1 on fu 0g u 0 on u 2 C 1;1 ( 1.4) The coincidence set is fu = 0g and the free boundary is fu = ....

J. Frehse, On the Regularity of the Solution of a Second Order Variational Inequality, Boll. Un. Mat. Ital. B (7) 6 (4), (1972), 312-315.

....# and w = 0, and its complement,# , where #u = 0 and therefore #w = ##. The interface between # and# is called the free boundary. The regularity of the membrane, u, has been studied by many people, and for an obstacle, #, in C 0,# or C 1,# , u will be as smooth as #. See [LS1] LS2] [Fj], BK] and [CK] On the other hand, no matter how smooth the obstacle is, the membrane will be no better than C 1,1 . People have also studied the geometry of the free boundary of the solution. In order to make this pursuit reasonable, however, other assumptions on the obstacle have to be ....

J. Frehse, On the regularity of the solution of a second order variational inequality, Boll. Un. Mat. Ital., (4)6(1972), 312--315.

....Contact point X Figure 3: Cusp The rst term in the energy (1.2) is a kind of elastic energy and the second term is a kind of gravity energy for a heavy membrane. The well posedness and good properties of the obstacle problem are garanteed by the following result for g 0: Theorem 1.1 (J. Frehse [11], C 1;1 Regularity of the Minimizer) There exists a unique solution u minimizing energy (1.2) on the convex set K de ned in (1.3) Moreover this solution satis es 8 : u = 1 on fu 0g u 0 on u 2 C 1;1 ( 1.4) The coincidence set is fu = 0g and the free boundary is fu = ....

J. Frehse, On the Regularity of the Solution of a Second Order Variational Inequality, Boll. Un. Mat. Ital. B (7) 6 (4), (1972), 312-315.

....in the most general case of Problem 3.1. 13 3.2 Proof of Theorem 1.1 The main advantage of the obstacle problem (1.1) 1.2) 1.3) compared to the more general free boundary problem (3. 1) is that there exists a unique weak solution (see [24, 11] and this solution is bounded in W 2;1 (see [11, 10, 3, 1]) As a consequence of this uniqueness the map t 7 u t 2W 2;p is continuous for every p2 (1; 1) Moreover from the nondegeneracy lemma (see Caffarelli [4] and for example [22] we have Lemma 3.2 Consider a solution of Problem (1.1) 1.2) 1.3) Under the assumptions of Theorem 1.1, for ....

Frehse J., On the Regularity of the Solution of a Second Order Variational Inequality, Boll. U.M.I., (4) 6, 312-315, (1972).

No context found.

J. Frehse, On the regularity of the solution of a second order variational inequality, Boll. Un. Mat. Ital., (4)6(1972), 312--315.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC