Book Review: Boundary-value problems with free boundaries for elliptic systems of equations
نویسندگان
چکیده
منابع مشابه
Boundary Value Problems for Elliptic Equations
where án, denotes differentiation in the direction of tlie normal to 8B . As is well known, there are explicit formulas for the solutions of the aboye problems, and one can then give a very careful analysis of the solutions when, say f E LP(áB, do), 1 < p < oo . In both cases, the boundary values are taken in the sense of non-tangential convergence, Le ., if Q E aB, and F(Q) _ F. (Q) _ {X E B1 ...
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Boundary regularity of solutions of the fully nonlinear boundary value problem F(x,u,Du, D2u) = 0 inn, G(x,u, Du) = 0 on dO is discussed for two-dimensional domains Q. The function F is assumed uniformly elliptic and G is assumed to depend (in a nonvacuous manner) on Du. Continuity estimates are proved for first and second derivatives of u under weak hypotheses for smoothness of F, G, and 0. In...
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Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3 with boundary ∂M . We denote the Ricci curvature, scalar curvature, mean curvature, and the second fundamental form by Ric, R , h, and Lαβ , respectively. The Yamabe problem for manifolds with boundary is to find a conformal metric ĝ = eg such that the scalar curvature is constant and the mean curvature is zero. The boundary is call...
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In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1985
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1985-15373-x