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A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line with the standard parabolic theory.
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참고문헌 (8)
참고문헌 신청
P. Friz / 2014 / A Course on Rough Paths / Springer
Martin Hairer / 2015 / A simple construction of the continuum parabolic Anderson model on R2 / Electronic Communications in Probability 20
Yaozhong Hu / 2015 / Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency / Electronic Journal of Probability 20
H.-J. Kim / 2017 / Time-homogeneous parabolic Wick–Anderson model in one space dimension: regularity of solution / Stochastics and Partial Differential Equations: Analysis and Computations 5(4):559~591
N. V. Krylov / 1996 / Lectures on Elliptic and Parabolic Equations in Holder spaces / American Mathematical Society :1090
Martin Hairer / 2015 / A simple construction of the continuum parabolic Anderson model on R2 / Electronic Communications in Probability 20
Yaozhong Hu / 2015 / Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency / Electronic Journal of Probability 20
H.-J. Kim / 2017 / Time-homogeneous parabolic Wick–Anderson model in one space dimension: regularity of solution / Stochastics and Partial Differential Equations: Analysis and Computations 5(4):559~591
N. V. Krylov / 1996 / Lectures on Elliptic and Parabolic Equations in Holder spaces / American Mathematical Society :1090
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