Boundary regularity for the supercritical Lane-Emden heat flow



We establish a Pacard-type monotonicity formula and Morrey bounds up to the boundary for smooth solutions of the Lane-Emden heat flow \(u_t-\Delta u = |u|^{p-2}u\) on a general, smoothly bounded domain \(\Omega \subset \mathbb {R}^n\), \(n\ge 3\), for exponents \(p>2^*=2n/(n-2)\), extending our previous work on the problem. As a consequence we obtain partially regular, self-similar tangent maps at any first blow-up point of the flow, and partial regularity at the blow-up time if the energy is uniformly bounded from below.

Mathematics Subject Classification

35K58 35K91 


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität SalzburgSalzburgAustria
  2. 2.Departement MathematikETH-ZürichZürichSwitzerland

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