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Displaying similar documents to “existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium”

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang (2014)

Studia Mathematica

Similarity:

We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

On elliptic systems pertaining to the Schrödinger equation

J. Chabrowski, E. Tonkes (2003)

Annales Polonici Mathematici

Similarity:

We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.