Regarding Anton Chekov's "The Lady with the Pet Dog," when the story was published in 1899, how was it received?

Anton Chekov achieved literary acclaim based on two forms
of writing he used: the play and the short story. Because Chekov was ill, fighting
tuberculosis, he moved to the region of Yalta in hopes of improving his health.  (The
short story mentioned in this post opens in Yalta.)

It was
here, in 1899, that he wrote and published, "The Lady with the Pet Dog." It is a sad
tale of Dmitri and Anna, both unhappily married to someone else, who happen to meet at a
vacation spot and begin an affair. They go their separate ways, but over time, they meet
again: both admit they have been unable to forget the other. Dmitri realizes he has
finally fallen in love, but the couple is unsure how to proceed, and the story ends on
that unresolved note.

"The Lady with the Pet Dog" was first
published in the magazine,  Russkaya Mysl (Russian
Thought). It is a much anthologized story; only four years later the story
was first published in English.

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[It] is considered one of Chekhov's best-known
stories.

And...

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In Yalta, Chekhov wrote one of his most famous
stories, The Lady with the Dog (also called Lady with
Lapdog), which depicts what at first seems a casual liaison between a married
man and a married woman in Yalta. Neither expects anything lasting from the encounter,
but they find themselves drawn back to each other, risking the security of their family
lives.