J. V. Prajapat

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We study the regularity of a parabolic free boundary problem of two-phase type with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the optimal C x ∩ C t -regularity of the solution and that the free boundary is, near the so-called branching points, the union of two graphs that are(More)
where h̄ is a continuous function. In the case 4(n− 1)h̄ n− 2 = Rg the scalar curvature, (1) is the Yamabe equation. Here, we assume h̄ a bounded function and h0 = ||h̄||L∞(M). The equation (1) has been well studied when M = Ω ⊂ R open, or M = Sn, see for example, [2]-[4], [12], [16] and references therein, where sup-inf inequality or Harnack type(More)
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