J. L. Lewis, Capacitary functions in convex rings, Arch. Rational Mech. Anal. 66 (1977), no. 3, 201-224. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
A Free Boundary Problem For ...-Laplace Equation - Manfredi, Petrosyan.. (Correct)
....K, i.e. a continuous function on n K such that p u = 0 in n K; u = 0 on ; u = 1 on K. Then q u 0; if 1 q p and q u 0; if p q 1: For the sake of completeness we present a proof since it will also help to understand Theorem 3.3 below. Proof. By a result of J. Lewis [Le], jruj 0 in nK and therefore u is real analytic in n K. Then, one can write p u in a nondivergence form p u = jruj p 2 ( u jruj 2 (p 2) 1u) 2.3) Let us introduce operators L p u : jruj 2 p p u = u jruj 2 (p 2) 1 u: 2.4) Then L q u has always the same sign as q u for ....
....p u = 0 in n K and hence L p u = 0, we deduce that L q u = jruj 2 (q p) 1u in n K: 2.5) Hence the lemma will follow as soon as we prove 1u 0: 2.6) To this end, take a point x 2 n K and choose a coordinate system centered at x such that the n axis is directed as ru. Let u(x) s. By [Le] the level set L s (u) fy : u(y) sg is convex and therefore its boundary s (u) L s (u) can be given near the point x as a graph fy : yn = f(y 0 )g of a convex C 1 function f in the coordinate system chosen above (here y 0 = y 1 ; yn 1 ) Di erentiating twice the identity ....
J. L. Lewis, Capacitary functions in convex rings, Arch. Rational Mech. Anal. 66 (1977), no. 3, 201-224.
A Free Boundary Problem for the p-Laplacian: Uniqueness.. - Acker, Meyer (1995) (Correct)
....of the operator permits this more general statement (see Remark 5. 2) We remark that there is substantial recent literature on the closely related problem of the convexity of level surfaces of solutions of elliptic partial differential equations in convex annular domains (see [CF] CS] KL] and [L1]) of which the work of Lewis [L1] is pertinent to the present study; in fact, our result follows by combining Lewis s result with certain aspects of the operator method. Remark 1.2 An additional interpretation of our model arises in the study of fluid flow through porous media. The linear flow ....
....general statement (see Remark 5. 2) We remark that there is substantial recent literature on the closely related problem of the convexity of level surfaces of solutions of elliptic partial differential equations in convex annular domains (see [CF] CS] KL] and [L1] of which the work of Lewis [L1] is pertinent to the present study; in fact, our result follows by combining Lewis s result with certain aspects of the operator method. Remark 1.2 An additional interpretation of our model arises in the study of fluid flow through porous media. The linear flow law in this case is called Darcy s ....
[Article contains additional citation context not shown here]
Lewis, J. L., Capacitary functions in convex rings, Arch. Rational Mech. Anal., 66(1977), 201-224.
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