Universal estimate of the gradient for parabolic equations
نویسنده
چکیده
We suggest a modification of the estimate for weighted L2-norm of the solution gradient of a parabolic equation via L2-norm of the free term. We found the limit upper estimate that can be achieved by transformation of the equation via adding a constant to the zero order coefficient. This upper limit estimate is used to obtain an asymptotic estimate for this weighted norm of the gradient at initial time. The diffusion coefficient of the parabolic equation is included into the estimate explicitly as the weight matrix in this norm for the gradient. The constants in these estimates are the same for all possible choices of the dimension, domain, time horizon, and the coefficients of the parabolic equation. AMS 2000 subject classification: 35K10, 35K15, 35K20
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