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We study fully nonlinear uniformly elliptic equations with measurable ingredients. Recently signiicant progress has been made in this area due to fundamental work of Caaarelli on W 2;p estimates for viscosity solutions. Here we present a uniied treatment of this theory based on an appropriate notion of viscosity solution. For instance, it is shown that… (More)

- Maciej Kocan
- 1995

We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations deened on the product of two innnite dimensional Hilbert spaces H 0 H 00 , where H 00 is separable. The equations have a special \separated" form in a sense that the terms involving second… (More)

The theory of fully nonlinear uniformly parabolic equations in spaces with Holder continuous derivatives is very well developed and can be found in the books of Krylov [21], Dong [11] and Lieberman [23]. Less is known when the equations themselves involve discontinuous functions and solutions are investigated from the point of view of Sobolev spaces. Basic… (More)

We consider a two-player, zero-sum diierential game governed by an abstract nonlinear diierential equation of accretive type in an innnite dimensional space. We prove that the value function of the game is the unique viscosity solution of the corresponding Hamilton-Jacobi-Isaacs equation in the sense of Crandall-Lions 12]. We also discuss some properties of… (More)

- Maciej Kocan
- Journal of personality assessment
- 1991

This article considers the three Rorschach tests obtained over an 8-year period for one female patient who struggled around her image of herself and others. Her struggle is revealed in the vicissitudes of the reflection responses over the three testings. A formulation is advanced regarding the meaning and significance of the reflection response as an… (More)

- Michael Crandall, Kar-Lung Fok, Maciej Kocan, SWIE

This paper provides a number of working tools for the discussion of fully nonlinear parabolic equations. These include: a proof that the maximum principle which provides L estimates of \strong" solutions of extremal equations by L norms of the forcing term over the \contact set" remains valid for viscosity solutions in an L sense, a gradient estimate in L… (More)

- G . CRANDALL, Patrick T . Fok, Maciej Kocan, A . SWIE
- 2007

This paper provides a number of working tools for the discussion of fully nonlinear parabolic equations. These include: a proof that the maximum principle which provides L 1 estimates of \strong" solutions of extremal equations by L n+1 norms of the forcing term over the \contact set" remains valid for viscosity solutions in an L n+1 sense, a gradient… (More)

We introduce the notion of a \good" solution of a fully nonlinear uniformly elliptic equation. It is proven that \good" solutions are equivalent to Lp-viscosity solutions of such equations. The main contribution of the paper is an explicit construction of elliptic equations with strong solutions that approximate any given fully nonlinear uniformly elliptic… (More)

- Maciej Kocan, Pierpaolo Soravia
- SIAM J. Control and Optimization
- 2000

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