Partial differential equations with minimal smoothness and applications
In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.
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Weakly elliptic systems with obstacle constraints
Some remarks on Widders theorem and uniqueness
On null sets of Pharmonic measures
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absolutely continuous Amer apply argument assume ball Banuelos boundary value problem Brownian motion coefficients compact conditioned Brownian motion conjecture constant C depending continuous function converges Cranston Dahlberg defined denote density Dhu(x dimension Dirichlet problem domain in Rn Editors eigenvalues elliptic equations elliptic operator estimate exists a constant Fabes Fefferman finite follows Fourier fundamental solution Green's function harmonic functions harmonic measure Harnack's inequality heat equation heat kernel Hence holds implies independent Kenig Laplacian Lebesgue measure Lemma linear Lipschitz domains Math Mathematics matrix maximum principle modulus of continuity mutually absolutely continuous nonnegative norm obtain open set p-harmonic parabolic measures Poisson kernel proof of Lemma proof of Theorem properties prove Theorem respect to Lebesgue result satisfies semigroup sequence smooth solution to Lu subset Suppose Theorem 2.1 Theory twist points uniformly vanishes vector Volume zero