共查询到20条相似文献,搜索用时 10 毫秒
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In this paper we complete the study of the regularity of the free boundary in two-phase problems for linear elliptic operators started in [M.C. Cerutti, F. Ferrari, S. Salsa, Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are C1,γ, Arch. Ration. Mech. Anal. 171 (2004) 329-348]. In particular we prove that Lipschitz and flat free boundaries (in a suitable sense) are smooth. As byproduct, we prove that Lipschitz free boundaries are smooth in the case of quasilinear operators of the form div(A(x,u)∇u) with Lipschitz coefficients. 相似文献
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Let u be the Newtonian potential of a real analytic distribution in an open set Ω. In this paper we assume u is analytically
continuable from the complement of Ω into some neighborhood of a point x0 ∈ ∂Ω, and we study conditions under which the analytic continuation implies that ∂Ω is a real analytic hypersurface in some
neighborhood of x0. 相似文献
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Brian Krummel 《Calculus of Variations and Partial Differential Equations》2014,51(3-4):525-537
Let \(N\) be a Riemannian manifold and consider a stationary union of three or more \(C^{1,\mu }\) hypersurfaces-with-boundary \(M_k \subset N\) with a common boundary \(\Gamma \) . We show that if \(N\) is smooth, then \(\Gamma \) is smooth and each \(M_k\) is smooth up to \(\Gamma \) (real analytic in the case \(N\) is real analytic). Consequently we strengthen a result of Wickramasekera for stable codimension 1 integral varifolds regularity to conclude that under the stronger hypothesis that \(V\) is a stationary, stable, integral \(n\) -varifold in an \((n+1)\) -dimensional, smooth (real analytic) Riemannian manifold such that the support of \(\Vert V\Vert \) is nowhere locally the union of three or more smooth (real analytic) hypersurfaces-with-boundary meeting along a common boundary, the singular set of \(V\) is empty if \(n \le 6\) , is discrete if \(n = 7\) , and has Hausdorff dimension at most \(n-7\) if \(n \ge 8\) . 相似文献
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A. L. Karakhanyan C. E. Kenig H. Shahgholian 《Calculus of Variations and Partial Differential Equations》2007,28(1):15-31
We show that the free boundary ∂{u > 0}, arising from the minimizer(s) u, of the functional
approaches the (smooth) fixed boundary ∂Ω tangentially, at points where the Dirichlet data vanishes along with its gradient.
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We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation
to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able
to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary. 相似文献
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Hans Wilhelm Alt 《Numerische Mathematik》1980,36(1):73-98
Summary A new numerical method is used to solve stationary free boundary problems for fluid flow through porous media. The method also applies to inhomogeneous media, and to cases with a partial unsaturated flow. 相似文献
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For a one-phase free boundary problem involving a fractional Laplacian, we prove that “flat free boundaries” are C1,α. We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian. 相似文献
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We study the regularity of the free boundary for solutions of the porous medium equation , , on , with initial data nonnegative and compactly supported. We show that, under certain assumptions on the initial data , the pressure will be smooth up to the interface , when , for some . As a consequence, the free-boundary is smooth.
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Institute of Mathematics and Cybernetics, Lithuanian Academy of Sciences. Vilnius University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 2, pp. 369–381, April–June, 1991. 相似文献
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Luis Caffarelli Arshak Petrosyan Henrik Shahgholian 《Journal of the American Mathematical Society》2004,17(4):827-869
We study the regularity of the free boundary in a Stefan-type problem
with no sign assumptions on and the time derivative .
with no sign assumptions on and the time derivative .