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Methods in Hilbert Spaces and Some Applications to Nonlinear Partial Differential Equations","{\"openalex\":\"W165234686\",\"doi\":\"10.1016/b978-0-12-775850-3.50009-1\"}","2026-05-19T11:58:16.191364503","2026-05-19T11:58:16.191570015","doi","10.1016/b978-0-12-775850-3.50009-1","arxivId","openalexId","W165234686","abstractText","publishedDate","1971-01-01","publishedYear",1971,"venue","Elsevier eBooks",414,"authors","keywords",[258,259,260],"pdfUrl","topVenue","Advanced Optimization Algorithms Research","Mathematical Inequalities and Applications","Optimization and Variational Analysis","paper_W1973359775","Remarks on sublinear elliptic equations","{\"openalex\":\"W1973359775\",\"doi\":\"10.1016/0362-546x(86)90011-8\"}","2026-05-16T03:58:22.230573407","2026-05-19T01:47:19.183483736","10.1016/0362-546x(86)90011-8","W1973359775","1986-01-01",1986,"Nonlinear Analysis",503,[273,274,275],"Nonlinear Partial Differential Equations","Advanced Mathematical Modeling in Engineering","Numerical methods in inverse problems","paper_W2067198640","A note on limiting cases of sobolev embeddings and convolution inequalities","{\"openalex\":\"W2067198640\",\"doi\":\"10.1080/03605308008820154\"}","2026-05-16T01:24:49.218321464","2026-05-21T18:23:35.180558974","10.1080/03605308008820154","W2067198640","(1980). A note on limiting cases of sobolev embeddings and convolution inequalities. Communications in Partial Differential Equations: Vol. 5, No. 7, pp. 773-789.","1980-01-01",1980,"Communications in Partial Differential Equations",521,[289,273,274],"Nonlinear Differential Equations Analysis","paper_W2135623248","Semi-linear second-order elliptic equations in L1","{\"openalex\":\"W2135623248\",\"doi\":\"10.2969/jmsj/02540565\"}","2026-05-15T17:52:50.227457771","2026-05-21T12:45:11.199269627","10.2969/jmsj/02540565","W2135623248","a paper which is yet to be completed, we have obtained some analogous results for parabolic equations.","1973-10-01",1973,"Journal of the Mathematical Society of Japan",562,[274,275,304],"https://projecteuclid.org/journals/journal-of-the-mathematical-society-of-japan/volume-25/issue-4/Semi-linear-second-order-elliptic-equations-in-L1/10.2969/jmsj/02540565.pdf","Differential Equations and Boundary Problems","paper_W2085787170","Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions","{\"openalex\":\"W2085787170\",\"doi\":\"10.1080/03605309108820797\"}","2026-05-15T16:29:09.223208351","2026-05-21T11:45:26.194781069","10.1080/03605309108820797","W2085787170","Click to increase image sizeClick to decrease image size Additional informationNotes on contributors","1991-01-01",1991,572,[273,289,274],"paper_W2058567087","Équations et inéquations non linéaires dans les espaces vectoriels en dualité","{\"openalex\":\"W2058567087\",\"doi\":\"10.5802/aif.280\"}","2026-05-15T02:20:17.231067046","2026-05-21T01:36:40.674965648","10.5802/aif.280","W2058567087","On introduit dans le cadre des espaces vectoriels en dualité, deux vastes classes d’opérateurs non linéaires les opérateurs de type M et les opérateurs pseudo-monotones. On met en évidence plusieurs de leurs propriétés analogues à celles des opérateurs monotones ; en particulier, on résoud pour ces opérateurs des problèmes abstraits de type elliptique et parabolique, des équations intégrales, des inéquations variationnelles stationnaires et d’évolution. Suivent quelques applications.","1968-01-01",1968,"Annales de l’institut Fourier",746,[289,331,274],"https://aif.centre-mersenne.org/item/10.5802/aif.280.pdf","Differential Equations and Numerical Methods","paper_W1499787021","Ginzburg-Landau Vortices","{\"openalex\":\"W1499787021\",\"doi\":\"10.1007/978-1-4612-0287-5\"}","2026-05-14T19:20:13.209626305","2026-05-20T19:52:48.185335416","10.1007/978-1-4612-0287-5","W1499787021","The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on modern materials research. The text is concerned with the study in two dimensions of stationary solutions uE of a complex valued Ginzburg-Landau equation involving a small parameter E. Such problems are related to questions occuring in physics, such as phase transistion phenomena in superconductors and superfluids. The parameter E has a dimension of a length, which is usually small. Thus, it should be of interest to study the asymptotics as E tends to zero. One of the main results asserts that the limit u* of minimizers uE exists. Moreover, u* is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree - or winding number - of the boundary condition. Each singularity has degree one - or, as physicists would say, vortices are quantized. The singularities have infinite energy, but after removing the core energy we are led to a concept of finite renormalized energy. The location of the singularities is completely determined by minimizing the renormalized energy among all possible configurations of defects. The limit u* can also be viewed as a geometrical object. It is a minimizing harmonic map into S1 with prescribed boundary condition g. Topological obstructions imply that every map u into S1 with u=g on the boundary must have infinite energy. Even though u* has infinite energy one can think of u* as having less infinite energy than any other map u with u=g on the boundary. The material presented in this book covers mostly recent and original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations and complex functions. It is designed for researchers and graduate students alike and can be used as a one-semester text.","1994-01-01",1994,"Birkhäuser Boston eBooks",859,[346,347,274],"https://link.springer.com/content/pdf/bfm:978-1-4612-0287-5/1?pdf=chapter%20toc","Nonlinear Dynamics and Pattern Formation","Theoretical and Computational Physics","paper_W1988167079","Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems","{\"openalex\":\"W1988167079\",\"doi\":\"10.1006/jfan.1994.1078\"}","2026-05-14T12:37:18.370988067","2026-05-21T16:29:01.186190167","10.1006/jfan.1994.1078","W1988167079","1994-06-01","Journal of Functional Analysis",1066,[304,274,273],"paper_W2066046051","A relation between pointwise convergence of functions and convergence of functionals","{\"openalex\":\"W2066046051\",\"doi\":\"10.1090/s0002-9939-1983-0699419-3\"}","2026-05-14T04:30:28.222909785","2026-05-21T06:41:19.209476643","10.1090/s0002-9939-1983-0699419-3","W2066046051","We show that if { f n } \\left \\{ {{f_n}} \\right \\} is a sequence of uniformly L p {L^p} -bounded functions on a measure space, and if f n → f {f_n} \\to f pointwise a.e., then lim n → ∞ { ‖ f n ‖ p p − ‖ f n − f ‖ p p } = ‖ f ‖ p p {\\lim _{n \\to \\infty }}\\left \\{ {\\left \\| {{f_n}} \\right \\|_p^p - \\left \\| {{f_n} - f} \\right \\|_p^p} \\right \\} = \\left \\| f \\right \\|_p^p for all 0 > p > ∞ 0 > p > \\infty . This result is also generalized in Theorem 2 to some functionals other than the L p {L^p} norm, namely ∫","1983-07-01",1983,"Proceedings of the American Mathematical Society",2037,[274,273,289],"https://www.ams.org/proc/1983-088-03/S0002-9939-1983-0699419-3/S0002-9939-1983-0699419-3.pdf","paper_W2038928461","Positive solutions of nonlinear elliptic equations involving critical sobolev exponents","{\"openalex\":\"W2038928461\",\"doi\":\"10.1002/cpa.3160360405\"}","2026-05-14T02:50:22.193259277","2026-05-21T04:44:53.186652614","10.1002/cpa.3160360405","W2038928461","Communications on Pure and Applied Mathematics",2898,[273,274,289],{"_59":384,"_61":385},[],[386],{"_64":387,"_66":388,"_68":389,"_70":390},1785434224247,{"_73":392,"_75":76,"_77":387,"_78":-5,"_79":26,"_80":26,"_81":26,"_82":-5,"_83":-5,"_84":85,"_35":86,"_87":88},[72,391],"[\"portal\",\"industries\"]","industries",[393,394,395,396,397,398,399,400,401,402,403,404],{"_15":466,"_29":467,"_31":-5,"_32":468,"_33":469,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":470,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":467,"_58":469},{"_15":462,"_29":463,"_31":-5,"_32":-5,"_33":464,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":465,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":463,"_58":464},{"_15":456,"_29":457,"_31":-5,"_32":458,"_33":459,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":460,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":457,"_58":459},{"_15":452,"_29":453,"_31":-5,"_32":-5,"_33":454,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":455,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":453,"_58":454},{"_15":448,"_29":449,"_31":-5,"_32":-5,"_33":450,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":451,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":449,"_58":450},{"_15":442,"_29":443,"_31":-5,"_32":444,"_33":445,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":446,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":443,"_58":445},{"_15":437,"_29":438,"_31":-5,"_32":-5,"_33":439,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":440,"_417":26,"_418":441,"_419":26,"_420":-5,"_57":438,"_58":439},{"_15":433,"_29":434,"_31":-5,"_32":-5,"_33":435,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":436,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":434,"_58":435},{"_15":429,"_29":430,"_31":-5,"_32":-5,"_33":431,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":432,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":430,"_58":431},{"_15":425,"_29":426,"_31":-5,"_32":-5,"_33":427,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":428,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":426,"_58":427},{"_15":421,"_29":422,"_31":-5,"_32":-5,"_33":423,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":424,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":422,"_58":423},{"_15":405,"_29":406,"_31":-5,"_32":-5,"_33":407,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":408,"_42":-5,"_44":-5,"_409":410,"_411":-5,"_412":76,"_413":414,"_415":416,"_417":26,"_418":85,"_419":26,"_420":-5,"_57":406,"_58":407},"tax_ind_smartphone","智能手机","Smartphone","manual","taxonomyType","INDUSTRY","code","level","parentId","tax_ind_root","path","科技行业/智能手机","sortOrder","isLeaf","entityCount","children","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算",true,"tax_ind_blockchain","区块链",[447],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[461],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[471,472],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_475":24},"SITE_BASE_URL"]

Haı̈m Brezis 人物

Haı̈m Brezis · 相关事件