منابع مشابه
A two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملTHE ONE PHASE FREE BOUNDARY PROBLEM FOR THE p-LAPLACIAN WITH NON-CONSTANT BERNOULLI BOUNDARY CONDITION
Our objective, here, is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a Bernoullitype boundary gradient condition and with the p-Laplacian as the governing operator. The main theorems of this paper assert that the exterior and the interior free boundary problem with a Bernoulli law, i.e. with a prescribed pressure a(x) on the “fr...
متن کاملSome Remarks on Stability of Cones for the One-phase Free Boundary Problem
We show that stable cones for the one-phase free boundary problem are hyperplanes in dimension 4. As a corollary, both one and two-phase energy minimizing hypersurfaces are smooth in dimension 4.
متن کاملOn smooth solutions to one phase free boundary problem in R
We construct a smooth axially symmetric solution to the classical one phase free boundary problem in R, n ≥ 3. Its free boundary is of “catenoid” type. This is a higher dimensional analogy of the HauswirthHelein-Pacard solution [18] in R. The existence of such solution is conjectured in [18, Remark 2.4]. This is the first nontrivial smooth solution to the one phase free boundary problem in high...
متن کاملA Two-phase Problem with a Lower-dimensional Free Boundary
For a bounded domain D ⊂ Rn, we study minimizers of the energy functional ∫ D |∇u| dx+ ∫ D∩(Rn−1×{0}) λχ{u>0} + λ χ{u<0} dHn−1, without any sign restriction on the function u. One of the main result states that the free boundaries Γ = ∂{u(·, 0) > 0} and Γ− = ∂{u(·, 0) < 0} never touch. Moreover, using Alexandrov-type reflection technique, we can show that in dimension n = 3 the free boundaries ...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Mathematica
سال: 2013
ISSN: 1239-629X,1798-2383
DOI: 10.5186/aasfm.2013.3815