Class information for:
Level 1: BERNOULLI PROBLEM//FREE BOUNDARY PROBLEM//FREE BOUNDARY

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
15989 679 17.5 44%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
94 3       MATHEMATICS//MATHEMATICS, APPLIED//MATH 76582
176 2             MATHEMATICS//VARIATIONAL METHODS//MATHEMATICS, APPLIED 22137
15989 1                   BERNOULLI PROBLEM//FREE BOUNDARY PROBLEM//FREE BOUNDARY 679

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 BERNOULLI PROBLEM authKW 418561 2% 85% 11
2 FREE BOUNDARY PROBLEM authKW 341772 12% 9% 84
3 FREE BOUNDARY authKW 303442 10% 10% 67
4 CONSTANT RANK THEOREM authKW 269819 1% 100% 6
5 BERNOULLI FREE BOUNDARY PROBLEM authKW 231271 1% 86% 6
6 MONOTONICITY FORMULA authKW 190888 2% 28% 15
7 CONVEXITY OF LEVEL SETS authKW 179879 1% 100% 4
8 CURVATURE ESTIMATES authKW 160593 1% 36% 10
9 POWER CONCAVITY authKW 143902 1% 80% 4
10 TRIAL METHOD authKW 134909 0% 100% 3

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 20367 74% 0% 502
2 Mathematics, Applied 13301 55% 0% 375
3 Mechanics 90 5% 0% 34
4 Mathematics, Interdisciplinary Applications 33 2% 0% 14
5 Automation & Control Systems 18 1% 0% 10
6 Engineering, General 14 2% 0% 11
7 Education, Scientific Disciplines 12 1% 0% 6
8 Statistics & Probability 9 1% 0% 10
9 Physics, Mathematical 5 1% 0% 10
10 Physics, Fluids & Plasmas 2 1% 0% 7

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MEFD 89940 0% 100% 2
2 MODELISAT MATH NUMER SCI INGN LAMSIN 89940 0% 100% 2
3 DIMAL DIPARTIMENTO MATEMAT INFORMAT U DINI 44970 0% 100% 1
4 DIP MATEMAT INFORMAT DINI 44970 0% 100% 1
5 HILL RUTGERS 44970 0% 100% 1
6 JOHANN RADON ANGEW MATH 44970 0% 100% 1
7 LR EM 44970 0% 100% 1
8 MATEMATIIKAN TILASTOTIETEEN LAITOS 44970 0% 100% 1
9 MODELISAT MATH NUMER SCI INGN LR99ES20 44970 0% 100% 1
10 RICHLAND RICHLAND 44970 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 INTERFACES AND FREE BOUNDARIES 55310 3% 6% 20
2 CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 25364 4% 2% 30
3 COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 18996 4% 2% 26
4 COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 18989 5% 1% 32
5 INDIANA UNIVERSITY MATHEMATICS JOURNAL 15860 4% 1% 29
6 ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 7754 3% 1% 21
7 NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 6227 6% 0% 41
8 ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE 5245 2% 1% 12
9 REVISTA BRASILEIRA DE ENSINO DE FISICA 4015 1% 1% 6
10 ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2790 1% 1% 7

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 BERNOULLI PROBLEM 418561 2% 85% 11 Search BERNOULLI+PROBLEM Search BERNOULLI+PROBLEM
2 FREE BOUNDARY PROBLEM 341772 12% 9% 84 Search FREE+BOUNDARY+PROBLEM Search FREE+BOUNDARY+PROBLEM
3 FREE BOUNDARY 303442 10% 10% 67 Search FREE+BOUNDARY Search FREE+BOUNDARY
4 CONSTANT RANK THEOREM 269819 1% 100% 6 Search CONSTANT+RANK+THEOREM Search CONSTANT+RANK+THEOREM
5 BERNOULLI FREE BOUNDARY PROBLEM 231271 1% 86% 6 Search BERNOULLI+FREE+BOUNDARY+PROBLEM Search BERNOULLI+FREE+BOUNDARY+PROBLEM
6 MONOTONICITY FORMULA 190888 2% 28% 15 Search MONOTONICITY+FORMULA Search MONOTONICITY+FORMULA
7 CONVEXITY OF LEVEL SETS 179879 1% 100% 4 Search CONVEXITY+OF+LEVEL+SETS Search CONVEXITY+OF+LEVEL+SETS
8 CURVATURE ESTIMATES 160593 1% 36% 10 Search CURVATURE+ESTIMATES Search CURVATURE+ESTIMATES
9 POWER CONCAVITY 143902 1% 80% 4 Search POWER+CONCAVITY Search POWER+CONCAVITY
10 TRIAL METHOD 134909 0% 100% 3 Search TRIAL+METHOD Search TRIAL+METHOD

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 HAMEL, F , NADIRASHVILI, N , SIRE, Y , (2016) CONVEXITY OF LEVEL SETS FOR ELLIPTIC PROBLEMS IN CONVEX DOMAINS OR CONVEX RINGS: TWO COUNTEREXAMPLES.AMERICAN JOURNAL OF MATHEMATICS. VOL. 138. ISSUE 2. P. 499 -527 30 88% 0
2 CHEN, CQ , (2014) ON THE MICROSCOPIC SPACETIME CONVEXITY PRINCIPLE OF FULLY NONLINEAR PARABOLIC EQUATIONS I: SPACETIME CONVEX SOLUTIONS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. VOL. 34. ISSUE 9. P. 3383 -3402 23 100% 0
3 CHEN, CQ , (2016) ON THE MICROSCOPIC SPACETIME CONVEXITY PRINCIPLE FOR FULLY NONLINEAR PARABOLIC EQUATIONS II: SPACETIME QUASICONCAVE SOLUTIONS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. VOL. 36. ISSUE 9. P. 4761 -4811 21 100% 0
4 CHEN, CQ , HU, BW , (2013) A MICROSCOPIC CONVEXITY PRINCIPLE FOR SPACETIME CONVEX SOLUTIONS OF FULLY NONLINEAR PARABOLIC EQUATIONS.ACTA MATHEMATICA SINICA-ENGLISH SERIES. VOL. 29. ISSUE 4. P. 651-674 22 85% 2
5 SHAHGHOLIAN, H , (2016) REGULARITY ISSUES FOR SEMILINEAR PDE-S (A NARRATIVE APPROACH).ST PETERSBURG MATHEMATICAL JOURNAL. VOL. 27. ISSUE 3. P. 577 -587 19 90% 0
6 ZHANG, T , ZHANG, W , (2013) ON CONVEXITY OF LEVEL SETS OF P-HARMONIC FUNCTIONS.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 255. ISSUE 7. P. 2065-2081 15 100% 0
7 SALANI, P , (2012) CONVEXITY OF SOLUTIONS AND BRUNN-MINKOWSKI INEQUALITIES FOR HESSIAN EQUATIONS IN R-3.ADVANCES IN MATHEMATICS. VOL. 229. ISSUE 3. P. 1924 -1948 23 64% 7
8 ISHIGE, K , NAKAGAWA, K , SALANI, P , (2016) POWER CONCAVITY IN WEAKLY COUPLED ELLIPTIC AND PARABOLIC SYSTEMS.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. VOL. 131. ISSUE . P. 81 -97 18 75% 0
9 SZEKELYHIDI, G , WEINKOVE, B , (2016) ON A CONSTANT RANK THEOREM FOR NONLINEAR ELLIPTIC PDES.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. VOL. 36. ISSUE 11. P. 6523 -6532 15 88% 0
10 HARBRECHT, H , MITROU, G , (2014) IMPROVED TRIAL METHODS FOR A CLASS OF GENERALIZED BERNOULLI PROBLEMS.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 420. ISSUE 1. P. 177 -194 15 88% 1

Classes with closest relation at Level 1


Rank Class id link
1 13801 INFINITY LAPLACIAN//VISCOSITY SOLUTIONS//FULLY NONLINEAR EQUATIONS
2 27842 MEASURE THEORY//EXISTENCE AND CONVERGENCE OF APPROXIMATE SOLUTIONS//EXTERIOR ELECTROMAGNETIC SHAPING
3 17113 MONGE AMPERE EQUATION//HESSIAN EQUATION//BERNSTEIN PROPERTY
4 22762 TWO PHASE CONDUCTORS//REARRANGEMENTS OF A FUNCTION//NANOSTRUCTURED QUANTUM DOTS
5 17321 OVERDETERMINED PROBLEMS//POMPEIU PROBLEM//OVERDETERMINED BOUNDARY VALUE PROBLEMS
6 11755 LIPSCHITZ DOMAINS//LAYER POTENTIALS//LAYER POTENTIAL OPERATORS
7 25451 SPREADING VANISHING DICHOTOMY//GLOBAL FAST SOLUTION//SPREADING AND VANISHING
8 15335 FRACTIONAL LAPLACIAN//FRACTIONAL P LAPLACIAN//FRACTIONAL SCHRODINGER EQUATION
9 20585 MAXIMAL L P L Q REGULARITY//DEGENERATE BOUNDARY CONDITION//BABUSKAS PARADOX
10 7592 VERY SINGULAR SOLUTION//FAST DIFFUSION//POROUS MEDIUM EQUATION

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