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- W2465730864 abstract "We consider elliptic equations of the form (E) $-Au=f(x,u)+mu$, where $A$ is a negative definite self-adjoint Dirichlet operator, $f$ is a function which is continuous and nonincreasing with respect to $u$ and $mu$ is a Borel measure of finite potential. We introduce a probabilistic definition of a solution of (E), develop the theory of good and reduced measures introduced by H. Brezis, M. Marcus and A.C. Ponce in the case where $A=Delta$ and show basic properties of solutions of (E). We also prove Kato's type inequality. Finally, we characterize the set of good measures in case $f(u)=-u^p$ for some $p>1$." @default.
- W2465730864 created "2016-07-22" @default.
- W2465730864 creator A5082571145 @default.
- W2465730864 date "2016-06-21" @default.
- W2465730864 modified "2023-09-27" @default.
- W2465730864 title "Reduced measures for semilinear elliptic equations involving Dirichlet operators" @default.
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- W2465730864 doi "https://doi.org/10.1007/s00526-016-1023-6" @default.
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