A negative result on regularity estimates on finite radial Morse index solutions to elliptic problems
J. Silverio Martinez-Baena; Salvador Villegas · 2024 · arXiv
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Abstract (excerpt)
In the regularity theory of solutions to elliptic partial differential equations often the concept of stability plays the role of a sufficient condition for smoothness. It is a natural question to ask if this holds true for nonstable but finite Morse index solutions. We provide a negative answer showing the existence of sequences of solutions with radial Morse index equal to 1 for which regularity estimates can not be satisfied.
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Metadata source: arXiv