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In particular, using a new three-spheres theorems for certain solutions of the above equation near zeta we prove that if V belongs to a certain Kato class near zeta and p>d (respectively, p<d), then any positive solution u of the equation Q'(u)=0 in a pu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.3873","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-23T17:56:56Z","cross_cats_sorted":[],"title_canon_sha256":"8e54f786f1cc0811d58c245490de5d84cb3f6d196f11962022934ea84a0dc3f8","abstract_canon_sha256":"a25a8b6e703e992cffc38323971ea6fc45a7a6989f3a466ceb18e2e069f59b1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:29.729998Z","signature_b64":"D7md7dMrSAIMGfuFuD+cS1SWVvcapZH1qLy0ZL1tXeSmPjXH8jncznMmde5t4GPdQPH4oiHPcnUadxccpDnhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8cfef3e2dd19688cdc032a2f69e7f6589714605a7652acb23a2c7c7700624d9","last_reissued_at":"2026-05-18T03:43:29.729527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:29.729527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isolated singularities of positive solutions of p-Laplacian type equations in R^d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martin Fraas, Yehuda Pinchover","submitted_at":"2010-08-23T17:56:56Z","abstract_excerpt":"We study the behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u) := -p-Laplacian(u) + V |u|^(p-2) u = 0 in Omega near an isolated singular point zeta, where 1 < p < inf, Omega is a domain in R^d with d > 1, and zeta = 0 or zeta = inf. 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