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- James Serrin
- 1996

We establish sharp capacitary estimates for Carnot-CarathÃ©odory rings associated to a system of vector fields of HÃ¶rmander type. Such estimates are instrumental to the study of the local behavior ofâ€¦ (More)

- James Serrin
- 2002

utt âˆ’âˆ†u+Q(t, x, ut) = f(x, u), u(0) = u0, ut(0) = u1, (1.1) in (0, T ) Ã— Rn, where 0 < T â‰¤ âˆž, n â‰¥ 1. The data u0 and u1 are in the energy space and are compactly supported in Rn. The terms Q and fâ€¦ (More)

- James Serrin
- 2010

Here R denotes an open set in the number space Â£n and u = u(x) is a realvalued function defined on R. The integrand f(x, u, p) is assumed to be nonnegative and continuous. Moreover, we supposeâ€¦ (More)

where Î² is an appropriate positive constant, see [1, 2, 4, 6, 7]. The question of uniqueness of ground states for (1.1) when f(u) has such exponential behavior has not previously been treated; theâ€¦ (More)

We show that the critical set generated by the Mountain Pass Theorem of Ambrosetti and Rabinowitz must have a well-defined structure. In particular, if the underlying Banach space is infiniteâ€¦ (More)

- D. Gilbarg, H Marie Jenkins, James Serrin, Jean Leray, Johannesand, Joachim Nitsche
- 2010

It is a well-known fact, documented by striking examples, that the solutions of sufficiently nonlinear elliptic differential equations behave quite differently from the solutions of linear ellipticâ€¦ (More)

- Patrizia Pucci, James Serrin
- SIAM J. Math. Analysis
- 2006

We consider divergence structure quasilinear singular elliptic partial differential equations on domains of Rn and show that there exist solutions with dead cores and, furthermore, solutions whichâ€¦ (More)

- Haim Brezis, James Serrin
- 2004

This paper concerns the problem of a flow past a given profile with prescribed velocity at infinity. In 1973 we announced (see [4]) a new approach-using variational inequalities-to the study in theâ€¦ (More)

Evolution Equations with Positive Initial Energy 243 with W , X Banach spaces and W â€², X â€² their duals. In order to define the energy Eu of a solution of (1.1), see below, it is necessary that thereâ€¦ (More)

- James Serrin
- 2014

A. Preface and introductory remarks B. The equation of motion I. Kinematics and dynamics of fluid motion II. Energy and momentum transfer III. Transformation of coordinates IV. Variational principlesâ€¦ (More)