
It is obtained qualitative sharp description of heat kernel \(G\) of Dirichlet Laplacian on bounded \(C^{1,1}\) domain \(D.\) There exists positive constants \(c_1, c_2\) such that, for \(\rho(x)=\text{dist}(x,\partial D)\) \[ \left[{\rho(x)\rho(y)\over t}\wedge 1\right]{c_1\over t^{n/2} } e^{-c_2|x-y|^2/t} \leq G(x,t;y,0)\leq \left[{\rho(x)\rho(y)\over t}\wedge 1\right]{1\over c_1 t^{n/2} } e^{-|x-y|^2/(c_2t)} \] for all \(x,y\in D\) and \(0
upper and lower estimates, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Initial value problems for second-order parabolic equations, Analysis
upper and lower estimates, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Initial value problems for second-order parabolic equations, Analysis
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